{"id":3198,"date":"2021-12-29T12:39:17","date_gmt":"2021-12-29T07:09:17","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=3198"},"modified":"2024-07-03T15:38:45","modified_gmt":"2024-07-03T10:08:45","slug":"ncert-solutions-for-class-11-maths-chapter-9-sequence-and-series-exercise-9-1","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/chapter-9-sequence-and-series-exercise-9-1\/","title":{"rendered":"NCERT Solutions for Class 11 Maths Chapter 9 Sequence and Series Exercise 9.1"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/chapter-9-sequence-and-series-exercise-9-1\/#NCERT_Solutions_for_Class_11_Maths_Chapter_9_Exercise_91\" title=\"NCERT Solutions for Class 11 Maths Chapter 9 Exercise 9.1\">NCERT Solutions for Class 11 Maths Chapter 9 Exercise 9.1<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/chapter-9-sequence-and-series-exercise-9-1\/#Access_NCERT_Solutions_for_Class_11_Maths_Chapter_9_Sequences_and_Series_Ex_91\" title=\"Access NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1\">Access NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>The <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\"><strong>NCERT Solutions<\/strong><\/a> for the first exercise of Class 11 Maths Chapter 9 are available here and can also be downloaded in PDF format. Chapter 9, Sequences and Series, is part of the <a href=\"https:\/\/infinitylearn.com\/surge\/cbse\/cbse-syllabus\/\"><strong>CBSE Syllabus<\/strong><\/a> for 2024-25. Exercise 9.1 of NCERT Solutions for Class 11 Maths covers the following topics:<\/p>\n<ul>\n<li>Introduction to Sequences and Series<\/li>\n<li>Sequences<\/li>\n<li>Series<\/li>\n<\/ul>\n<p>The <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-books\/\"><strong>NCERT textbook<\/strong><\/a> includes numerous questions for students to solve and practice. To achieve high marks in the Class 11 examination, it is essential to solve and practice the <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/\"><strong>NCERT Solutions for Class 11 Maths<\/strong><\/a>.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_11_Maths_Chapter_9_Exercise_91\"><\/span>NCERT Solutions for Class 11 Maths Chapter 9 Exercise 9.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download the free PDF of NCERT Solutions for Class 11 Maths Chapter 9 Exercise 9.1, prepared by expert Mathematics teachers at Infinity Learn, following CBSE (NCERT) guidelines. Access our Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 solutions to help you revise the entire syllabus and score higher marks in your exams.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Access_NCERT_Solutions_for_Class_11_Maths_Chapter_9_Sequences_and_Series_Ex_91\"><\/span>Access NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1. Write the first five terms of each of the sequences in Exercises 1 to 6 whose nth terms are:<\/strong><strong> a<sub>n<\/sub> = n (n + 2) <\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given,<\/p>\n<p>n<sup>th<\/sup> term of a sequence a<sub>n<\/sub> = n (n + 2)<\/p>\n<p>On substituting <em>n<\/em> = 1, 2, 3, 4, and 5, we get the first five terms<\/p>\n<p>a<sub>1<\/sub> = 1(1 + 2) = 3<\/p>\n<p>a<sub>2<\/sub> = 2(2 + 2) = 8<\/p>\n<p>a<sub>3<\/sub> = 3(3 + 2) = 15<\/p>\n<p>a<sub>4<\/sub> = 4(4 + 2) = 24<\/p>\n<p>a<sub>5<\/sub> = 5(5 + 2) = 35<\/p>\n<p>Hence, the required terms are 3, 8, 15, 24, and 35.<\/p>\n<p><strong>2. Find the indicated terms in each of the sequences in Exercises 7 to 10 whose n<sup>th<\/sup> terms are:<\/strong><\/p>\n<p><strong>1. a<sub>n<\/sub> = 4n \u2013 3; a<sub>17<\/sub>, a<sub>24<\/sub><\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given,<\/p>\n<p><em>n<\/em><sup>th<\/sup> term of the sequence is a<sub>n<\/sub> = 4n \u2013 3<\/p>\n<p>On substituting <em>n<\/em> = 17, we get<\/p>\n<p>a<sub>17<\/sub> = 4(17) \u2013 3 = 68 \u2013 3 = 65<\/p>\n<p>Next, on substituting <em>n<\/em> = 24, we get<\/p>\n<p>a<sub>24<\/sub> = 4(24) \u2013 3 = 96 \u2013 3 = 93<\/p>\n<p><strong>2. a<sub>n<\/sub> = n<sup>2<\/sup>\/2<sup>n<\/sup> ; a<sup>7<\/sup><\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given,<\/p>\n<p><em>n<\/em><sup>th<\/sup> term of the sequence is a<sub>n<\/sub> = n<sup>2<\/sup>\/2<sup>n<\/sup><\/p>\n<p>Now, on substituting <em>n<\/em> = 7, we get<\/p>\n<p>a<sub>7<\/sub> = 7<sup>2<\/sup>\/2<sup>7<\/sup> = 49\/ 128<\/p>\n<p><strong>3. Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series:<\/strong><\/p>\n<p><strong>11. a<sub>1<\/sub> = 3, a<sub>n<\/sub> = 3a<sub>n-1<\/sub> + 2 for all n &gt; 1<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given, a<sub>n<\/sub> = 3a<sub>n-1<\/sub> + 2 and a<sub>1<\/sub> = 3<\/p>\n<p>Then,<\/p>\n<p>a<sub>2<\/sub> = 3a<sub>1<\/sub> + 2 = 3(3) + 2 = 11<\/p>\n<p>a<sub>3<\/sub> = 3a<sub>2<\/sub> + 2 = 3(11) + 2 = 35<\/p>\n<p>a<sub>4<\/sub> = 3a<sub>3<\/sub> + 2 = 3(35) + 2 = 107<\/p>\n<p>a<sub>5<\/sub> = 3a<sub>4<\/sub> + 2 = 3(107) + 2 = 323<\/p>\n<p>Thus, the first 5 terms of the sequence are 3, 11, 35, 107 and 323.<\/p>\n<p>Hence, the corresponding series is<\/p>\n<p>3 + 11 + 35 + 107 + 323 \u2026\u2026.<\/p>\n<p><strong>12. a<sub>1<\/sub> = -1, a<sub>n<\/sub> = a<sub>n-1<\/sub>\/n, n \u2265 2<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given,<\/p>\n<p>a<sub>n<\/sub> = a<sub>n-1<\/sub>\/n and a<sub>1<\/sub> = -1<\/p>\n<p>Then,<\/p>\n<p>a<sub>2<\/sub> = a<sub>1<\/sub>\/2 = -1\/2<\/p>\n<p>a<sub>3<\/sub> = a<sub>2<\/sub>\/3 = -1\/6<\/p>\n<p>a<sub>4<\/sub> = a<sub>3<\/sub>\/4 = -1\/24<\/p>\n<p>a<sub>5<\/sub> = a<sub>4<\/sub>\/5 = -1\/120<\/p>\n<p>Thus, the first 5 terms of the sequence are -1, -1\/2, -1\/6, -1\/24 and -1\/120.<\/p>\n<p>Hence, the corresponding series is<\/p>\n<p>-1 + (-1\/2) + (-1\/6) + (-1\/24) + (-1\/120) + \u2026\u2026.<\/p>\n<p><strong>13. a<sub>1<\/sub> = a<sub>2 <\/sub>= 2, a<sub>n<\/sub> = a<sub>n-1<\/sub> \u2013 1, n &gt; 2<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given,<\/p>\n<p>a<sub>1<\/sub> = a<sub>2<\/sub>, a<sub>n<\/sub> = a<sub>n-1<\/sub> \u2013 1<\/p>\n<p>Then,<\/p>\n<p>a<sub>3<\/sub> = a<sub>2<\/sub> \u2013 1 = 2 \u2013 1 = 1<\/p>\n<p>a<sub>4<\/sub> = a<sub>3<\/sub> \u2013 1 = 1 \u2013 1 = 0<\/p>\n<p>a<sub>5<\/sub> = a<sub>4<\/sub> \u2013 1 = 0 \u2013 1 = -1<\/p>\n<p>Thus, the first 5 terms of the sequence are 2, 2, 1, 0 and -1.<\/p>\n<p>The corresponding series is<\/p>\n<p>2 + 2 + 1 + 0 + (-1) + \u2026\u2026<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The NCERT Solutions for the first exercise of Class 11 Maths Chapter 9 are available here and can also be [&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":"NCERT Solutions for Class 11 Maths","_yoast_wpseo_title":"NCERT Solutions for Class 11 Maths Ch- 9 Exercise 9.1","_yoast_wpseo_metadesc":"Access the NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series, Exercise 9.1, prepared by subject experts. 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