{"id":30427,"date":"2022-01-29T15:59:33","date_gmt":"2022-01-29T10:29:33","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=30427"},"modified":"2025-10-23T13:36:46","modified_gmt":"2025-10-23T08:06:46","slug":"arithmetic-progressions-class-10-extra-questions-maths-chapter-5","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-material\/maths\/class-10\/arithmetic-progressions-class-10-extra-questions-maths-chapter-5\/","title":{"rendered":"Important Questions for Class 10 Maths Chapter 5: Arithmetic Progression"},"content":{"rendered":"<p>Important questions for Class 10 Maths Chapter 5 on Arithmetic Progression are available here to help students get ready for the 2024-2025 board exams. These questions follow the <strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-books\/\" target=\"_blank\" rel=\"noopener\">NCERT book<\/a><\/strong> and <strong><a href=\"https:\/\/infinitylearn.com\/surge\/cbse\/cbse-syllabus\/\" target=\"_blank\" rel=\"noopener\">CBSE syllabus<\/a><\/strong>. We&#8217;ve made these questions based on the exam style, past papers, exam trends, and the latest 2024-25 sample papers. Solving these questions can help students get high scores in their Maths exams. They can also check their answers using the provided solutions. So, it&#8217;s a good idea for students to practice these questions well. This will boost their confidence and improve their skills.<\/p>\n<h2>Important Questions For Class 10 Chapter 5 With Solutions<\/h2>\n<p><strong>Question:<\/strong> Define Arithmetic Progression (AP).<\/p>\n<p><strong>Answer:<\/strong> Arithmetic Progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant.<\/p>\n<p><strong>Question:<\/strong> What is the common difference in an AP?<\/p>\n<p><strong>Answer:<\/strong> The common difference in an AP is the constant value by which each term differs from its preceding term.<\/p>\n<p><strong>Question: Which term of the AP 3, 15, 27, 39, \u2026 will be 132 more than its 54th term?<\/strong><\/p>\n<p><strong>Answer: <\/strong>Given AP is: 3, 15, 27, 39, \u2026<br \/>\nFirst term, a = 3<br \/>\nCommon difference, d = a<sub>2<\/sub> \u2212 a<sub>1<\/sub> = 15 \u2212 3 = 12<\/p>\n<p>We know that,<br \/>\na<sub>n<\/sub> = a + (n \u2212 1) d<\/p>\n<p>Therefore,<\/p>\n<p>a<sub>54<\/sub> = a + (54 \u2212 1) d<br \/>\n= 3 + (53) (12)<br \/>\n= 3 + 636<br \/>\na<sub>54<\/sub> = 639<\/p>\n<p>We have to find the term of this AP.which is 132 more than a<sub>54<\/sub>, i.e. 771.<br \/>\nLet nth term be 771.<br \/>\na<sub>n<\/sub> = a + (n \u2212 1) d<br \/>\n771 = 3 + (n \u2212 1) 12<br \/>\n768 = (n \u2212 1) 12<br \/>\n\u21d2 (n \u2212 1) = 64<br \/>\n\u21d2 n = 65<\/p>\n<p>Therefore, the 65th term is 132 more than the 54th term of the given AP.<\/p>\n<p><strong>Alternate Method:<\/strong><\/p>\n<p>Let nth term be 132 more than 54th term.<br \/>\nn = 54 + (132\/12)<\/p>\n<p>= 54 + 11<\/p>\n<p>= 65th term<\/p>\n<p><strong>Question:<\/strong> If the first term of an AP is &#8216;a&#8217; and the common difference is &#8216;d&#8217;, what is the nth term of the AP?<\/p>\n<p><strong>Answer:<\/strong> The nth term<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mi>\ud835\udc5b<\/mi><\/msub><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> of an AP is given by the formula<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mi>\ud835\udc5b<\/mi><\/msub><mo>=<\/mo><mi>\ud835\udc4e<\/mi><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mi>\ud835\udc5b<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mi>\ud835\udc51<\/mi><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><\/span><\/span>.<\/p>\n<p><strong>Question:  Check whether \u2013 150 is a term of the AP: 11, 8, 5, 2 . . .<\/strong><\/p>\n<p><strong>Answer:<\/strong>  Given AP: 11, 8, 5, 2, \u2026<\/p>\n<p>First term, a = 11<\/p>\n<p>Common difference, d = a<sub>2<\/sub> \u2212 a<sub>1<\/sub> = 8 \u2212 11 = \u22123<\/p>\n<p>Let \u2212150 be the nth term of this AP.<\/p>\n<p>As we know, for an AP,<\/p>\n<p>a<sub>n<\/sub> = a + (n \u2212 1) d<\/p>\n<p>-150 = 11 + (n \u2013 1)(-3)<\/p>\n<p>-150 = 11 \u2013 3n + 3<\/p>\n<p>\u21d2 -164 = -3n<\/p>\n<p>\u21d2 n = 164\/3<\/p>\n<p>Clearly, n is not an integer but a fraction.<\/p>\n<p>Therefore, \u2013 150 is not a term of the given AP.<\/p>\n<p><strong>Question:<\/strong> How can you find the number of terms in an AP when given the first term, last term, and common difference?<\/p>\n<p><strong>Answer:<\/strong> The number of terms in an AP can be found using the formula<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ud835\udc5b<\/mi><mo>=<\/mo><mfrac><mrow><mi>\ud835\udc59<\/mi><mo>\u2212<\/mo><mi>\ud835\udc4e<\/mi><\/mrow><mi>\ud835\udc51<\/mi><\/mfrac><mo>+<\/mo><mn>1<\/mn><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">l<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ud835\udc4e<\/mi><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span> is the first term,<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ud835\udc59<\/mi><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">l<\/span><\/span><\/span> is the last term, and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ud835\udc51<\/mi><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">d<\/span><\/span><\/span> is the common difference.<\/p>\n<p><strong>Question:<\/strong> What is the sum of the first &#8216;n&#8217; terms of an AP?<\/p>\n<p><strong>Answer:<\/strong> The sum<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc46<\/mi><mi>\ud835\udc5b<\/mi><\/msub><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> of the first &#8216;n&#8217; terms of an AP is given by the formula<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc46<\/mi><mi>\ud835\udc5b<\/mi><\/msub><mo>=<\/mo><mfrac><mi>\ud835\udc5b<\/mi><mn>2<\/mn><\/mfrac><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>\ud835\udc4e<\/mi><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mi>\ud835\udc5b<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mi>\ud835\udc51<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mclose\">)<\/span><\/span><\/span>.<\/p>\n<p><strong>Question:<\/strong> If the 5th term of an AP is 17 and the 10th term is 32, find the common difference.<\/p>\n<p><strong>Answer:<\/strong><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ud835\udc51<\/mi><mo>=<\/mo><mfrac><mrow><msub><mi>\ud835\udc47<\/mi><mn>10<\/mn><\/msub><mo>\u2212<\/mo><msub><mi>\ud835\udc47<\/mi><mn>5<\/mn><\/msub><\/mrow><mrow><mn>10<\/mn><mo>\u2212<\/mo><mn>5<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>32<\/mn><mo>\u2212<\/mo><mn>17<\/mn><\/mrow><mn>5<\/mn><\/mfrac><mo>=<\/mo><mn>3<\/mn><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">d<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">10<span class=\"mbin mtight\">\u2212<\/span>5<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">T<\/span><span class=\"msupsub\"><span class=\"sizing reset-size3 size1 mtight\">10<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\">T<\/span><span class=\"msupsub\"><span class=\"sizing reset-size3 size1 mtight\">5<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">5<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">32<span class=\"mbin mtight\">\u2212<\/span>17<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span>.<\/p>\n<p><strong>Question:<\/strong> If the sum of 4th and 9th terms of an AP is 60 and the common difference is 3, find the first term.<\/p>\n<p><strong>Answer:<\/strong> Using<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mn>4<\/mn><\/msub><mo>=<\/mo><mi>\ud835\udc4e<\/mi><mo>+<\/mo><mn>3<\/mn><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">4<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span> and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mn>9<\/mn><\/msub><mo>=<\/mo><mi>\ud835\udc4e<\/mi><mo>+<\/mo><mn>3<\/mn><mo stretchy=\"false\">(<\/mo><mn>9<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">9<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">9<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span>, we get<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ud835\udc4e<\/mi><mo>=<\/mo><mn>8<\/mn><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">8<\/span><\/span><\/span>.<\/p>\n<p><strong>Question:<\/strong> If the 12th term of an AP is 29 and the common difference is 2, find the 7th term.<\/p>\n<p><strong>Answer:<\/strong> Using<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mn>7<\/mn><\/msub><mo>=<\/mo><mi>\ud835\udc4e<\/mi><mo>+<\/mo><mn>6<\/mn><mi>\ud835\udc51<\/mi><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">7<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><span class=\"mord mathnormal\">d<\/span><\/span><\/span>, we get<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mn>7<\/mn><\/msub><mo>=<\/mo><mn>29<\/mn><mo>\u2212<\/mo><mn>10<\/mn><mo>=<\/mo><mn>19<\/mn><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">7<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">29<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">10<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">19<\/span><\/span><\/span>.<\/p>\n<p><strong>Question:<\/strong> If the first term of an AP is 4 and the 8th term is 22, find the common difference.<\/p>\n<p><strong>Answer:<\/strong><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ud835\udc51<\/mi><mo>=<\/mo><mfrac><mrow><msub><mi>\ud835\udc47<\/mi><mn>8<\/mn><\/msub><mo>\u2212<\/mo><mi>\ud835\udc4e<\/mi><\/mrow><mrow><mn>8<\/mn><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>22<\/mn><mo>\u2212<\/mo><mn>4<\/mn><\/mrow><mn>7<\/mn><\/mfrac><mo>=<\/mo><mn>2<\/mn><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">d<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">8<span class=\"mbin mtight\">\u2212<\/span>1<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">T<\/span><span class=\"msupsub\"><span class=\"sizing reset-size3 size1 mtight\">8<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">7<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">22<span class=\"mbin mtight\">\u2212<\/span>4<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><\/span><\/span>.<\/p>\n<p><strong>Question:<\/strong> What is the formula for the nth term of an AP in terms of the first term, common difference, and number of terms?<\/p>\n<p><strong>Answer:<\/strong><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mi>\ud835\udc5b<\/mi><\/msub><mo>=<\/mo><mi>\ud835\udc4e<\/mi><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mi>\ud835\udc5b<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mi>\ud835\udc51<\/mi><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><\/span><\/span>.<\/p>\n<p><strong>Question:<\/strong> How can you determine if a given sequence of numbers is an AP?<\/p>\n<p><strong>Answer:<\/strong> Check if the difference between consecutive terms is constant. If it is, the sequence is an AP.<\/p>\n<p><strong>Question:<\/strong> What is the sum of an AP if its first term is 3, common difference is 4, and it has 10 terms?<\/p>\n<p><strong>Answer:<\/strong><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc46<\/mi><mn>10<\/mn><\/msub><mo>=<\/mo><mfrac><mn>10<\/mn><mn>2<\/mn><\/mfrac><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>10<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>245<\/mn><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">10<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">10<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">10<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">4<\/span><span class=\"mclose\">))<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">245<\/span><\/span><\/span>.<\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/study-material\/surface-areas-and-volumes\/class-10\/extra-questions\/maths\/chapter-13\/\" target=\"_blank\" rel=\"noopener\">Surface Areas and Volumes Class 10 Extra Questions Maths Chapter 13<\/a><\/strong><\/p>\n<p><strong>Question:<\/strong> If the sum of first &#8216;n&#8217; terms of an AP is<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc46<\/mi><mi>\ud835\udc5b<\/mi><\/msub><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>, what is<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc46<\/mi><mi>\ud835\udc5b<\/mi><\/msub><mo>\u2212<\/mo><msub><mi>\ud835\udc46<\/mi><mrow><mi>\ud835\udc5b<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span>1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>?<\/p>\n<p><strong>Answer:<\/strong><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc46<\/mi><mi>\ud835\udc5b<\/mi><\/msub><mo>\u2212<\/mo><msub><mi>\ud835\udc46<\/mi><mrow><mi>\ud835\udc5b<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><msub><mi>\ud835\udc47<\/mi><mi>\ud835\udc5b<\/mi><\/msub><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span>1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/p>\n<p><strong>Question:<\/strong> What is the sum of all odd terms in an AP?<\/p>\n<p><strong>Answer:<\/strong><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc46<\/mi><mtext>odd<\/mtext><\/msub><mo>=<\/mo><mfrac><mi>\ud835\udc5b<\/mi><mn>2<\/mn><\/mfrac><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>\ud835\udc4e<\/mi><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mi>\ud835\udc5b<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mi>\ud835\udc51<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\">odd<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mclose\">)<\/span><\/span><\/span> where &#8216;n&#8217; is the number of odd terms.<\/p>\n<p><strong>Question: How many terms of the AP : 24, 21, 18, . . . must be taken so that their sum is 78?<\/strong><\/p>\n<p><strong>Answer: <\/strong>Given AP: 24, 21, 18,\u2026<\/p>\n<p>Here, a = 24, d = 21 \u2013 24 = \u20133, S<sub>n<\/sub> = 78. We need to find n.<br \/>\nWe know that;<\/p>\n<p>S<sub>n<\/sub> = n\/2[2a + (n \u2013 1)d]\n<p>So, 78 = n\/2 [48 + (n \u2013 1)(-3)]\n<p>78 = n\/2 [51 \u2013 3n]\n<p>156 = 51n \u2013 3n<sup>2<\/sup><\/p>\n<p>3n<sup>2<\/sup> \u2013 51n + 156 = 0<\/p>\n<p>n<sup>2<\/sup> \u2013 17n + 52 = 0<\/p>\n<p>n<sup>2<\/sup> \u2013 13n \u2013 4n + 52 = 0<\/p>\n<p>n(n \u2013 13) \u2013 4(n \u2013 13) = 0<\/p>\n<p>(n \u2013 4) (n \u2013 13) = 0<\/p>\n<p>n = 4 or 13<br \/>\nBoth values of n are admissible. So, the number of terms is either 4 or 13.<\/p>\n<p><strong>Question:<\/strong> If the 3rd term of an AP is 8 and the 6th term is 20, find the 10th term.<\/p>\n<p><strong>Answer:<\/strong> Using<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mn>3<\/mn><\/msub><mo>=<\/mo><mi>\ud835\udc4e<\/mi><mo>+<\/mo><mn>2<\/mn><mi>\ud835\udc51<\/mi><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">d<\/span><\/span><\/span> and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mn>6<\/mn><\/msub><mo>=<\/mo><mi>\ud835\udc4e<\/mi><mo>+<\/mo><mn>5<\/mn><mi>\ud835\udc51<\/mi><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">6<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mord mathnormal\">d<\/span><\/span><\/span>, we find<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mn>10<\/mn><\/msub><mo>=<\/mo><mn>34<\/mn><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">10<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">34<\/span><\/span><\/span>.<\/p>\n<p><strong>Question:<\/strong> What is the 30th term of an AP if the 10th term is 20 and the common difference is 3?<\/p>\n<p><strong>Answer:<\/strong><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mn>30<\/mn><\/msub><mo>=<\/mo><mn>20<\/mn><mo>+<\/mo><mn>20<\/mn><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>80<\/mn><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">30<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">20<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">20<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">80<\/span><\/span><\/span>.<\/p>\n<p><strong>Question:<\/strong> How can you find the common difference if given the first and third terms of an AP?<\/p>\n<p><strong>Answer:<\/strong><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ud835\udc51<\/mi><mo>=<\/mo><msub><mi>\ud835\udc47<\/mi><mn>3<\/mn><\/msub><mo>\u2212<\/mo><mi>\ud835\udc4e<\/mi><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">d<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span>.<\/p>\n<p><strong>Question:<\/strong> If the sum of the first 5 terms of an AP is 60 and the sum of the first 10 terms is 210, find the sum of the next 5 terms.<\/p>\n<p><strong>Answer:<\/strong><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc46<\/mi><mn>10<\/mn><\/msub><mo>\u2212<\/mo><msub><mi>\ud835\udc46<\/mi><mn>5<\/mn><\/msub><mo>=<\/mo><mn>210<\/mn><mo>\u2212<\/mo><mn>60<\/mn><mo>=<\/mo><mn>150<\/mn><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">10<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">5<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">210<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">60<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">150<\/span><\/span><\/span>.<\/p>\n<p><strong>Question:<\/strong> What is the 12th term of an AP if the 15th term is 55 and the common difference is 3?<\/p>\n<p><strong>Answer:<\/strong><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mn>12<\/mn><\/msub><mo>=<\/mo><mn>55<\/mn><mo>\u2212<\/mo><mn>3<\/mn><mo stretchy=\"false\">(<\/mo><mn>15<\/mn><mo>\u2212<\/mo><mn>12<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>46<\/mn><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">12<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">55<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">15<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">12<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">46<\/span><\/span><\/span>.<\/p>\n<p><strong>Question:<\/strong> If the 4th term of an AP is 9 and the 7th term is 15, find the first term and common difference.<\/p>\n<p><strong>Answer:<\/strong> Using<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mn>4<\/mn><\/msub><mo>=<\/mo><mi>\ud835\udc4e<\/mi><mo>+<\/mo><mn>3<\/mn><mi>\ud835\udc51<\/mi><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mord mathnormal\">d<\/span><\/span><\/span> and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ud835\udc47<\/mi><mn>7<\/mn><\/msub><mo>=<\/mo><mi>\ud835\udc4e<\/mi><mo>+<\/mo><mn>6<\/mn><mi>\ud835\udc51<\/mi><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">7<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><span class=\"mord mathnormal\">d<\/span><\/span><\/span>, we find<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ud835\udc4e<\/mi><mo>=<\/mo><mn>3<\/mn><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span> and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ud835\udc51<\/mi><mo>=<\/mo><mn>2<\/mn><\/mrow><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">d<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><\/span><\/span>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Important questions for Class 10 Maths Chapter 5 on Arithmetic Progression are available here to help students get ready for [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Arithmetic Progressions Class 10","_yoast_wpseo_title":"Important Questions For Class 10 Chapter 5 With Solutions - Arithmetic Progression","_yoast_wpseo_metadesc":"Get Arithmetic Progressions Class 10 Extra Questions Maths Chapter. Click Here To Get The List Of Topics And Ideas At infinitylearn.com","custom_permalink":"study-material\/maths\/class-10\/arithmetic-progressions-class-10-extra-questions-maths-chapter-5\/"},"categories":[13,21],"tags":[7873,7874],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Important Questions For Class 10 Chapter 5 With Solutions - Arithmetic Progression<\/title>\n<meta name=\"description\" content=\"Get Arithmetic Progressions Class 10 Extra Questions Maths Chapter. 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