RD Sharma Class 10 Solutions Chapter 9 Arithmetic Progressions

RD Sharma Solutions for Class 10 Maths Chapter 9 – Arithmetic Progressions are made available here to help students prepare effectively and excel in their board exams. To perform well in the Class 10 Mathematics examination, it’s important to understand concepts in a structured and systematic manner. The RD Sharma Solutions perfectly meet this requirement, providing students with clear and detailed methods to secure high marks in their final exams.

The solutions, thoughtfully prepared by the expert team at Infinity Learn, are presented in simple language with step-by-step explanations. This approach ensures that students gain complete clarity on all the important concepts covered in Chapter 9 – Arithmetic Progressions.

Arithmetic Progressions is one of the more interesting and scoring chapters in Class 10 Maths. However, due to common misconceptions, many students miss out on full marks. To address this, the RD Sharma Solutions for Class 10 offer well-explained answers for all six exercises in the chapter, making it easier for students to build a strong foundation.

The key learning points in this chapter include:

• Understanding the concept of sequences
• Defining and identifying Arithmetic Progressions (A.P.)
• Expressing sequences through an algebraic formula for terms
• Finding the sum of terms in an Arithmetic Progression
• Solving a variety of word problems based on real-life applications of A.P.

By practicing regularly with these solutions, students can confidently master the topic and enhance their performance in the board exams.

Download RD Sharma Class 10 Chapter 9 Arithmetic Progression PDF

Access RD Sharma Solutions for Class 10 Maths CBSE Chapter 9 - Arithmetic Progression

1. Find the 10th term of the A.P.: 2, 7, 12, 17, ...

Solution:

a = 2, d = 5

Using formula: a_n = a + (n-1)d

a₁₀ = 2 + (10-1) × 5 = 47

2. Find the sum of the first 15 terms of the A.P.: 5, 8, 11, 14, ...

Solution:

a = 5, d = 3, n = 15

S₁₅ = (15/2)[2(5) + (15-1)×3] = 390

3. Which term of the A.P. 7, 13, 19, 25, ... is 79?

Solution:

a = 7, d = 6

a + (n-1)d = 79 ⇒ n = 13

4. Find the 20th term of the A.P.: 3, 5, 7, 9, ...

Solution:

a = 3, d = 2

a₂₀ = 3 + (20-1) × 2 = 41

5. Find the sum of the first 12 terms of the A.P.: 10, 15, 20, 25, ...

Solution:

a = 10, d = 5, n = 12

S₁₂ = (12/2)[2(10) + (12-1)×5] = 450

6. Find the 15th term of the A.P. whose first term is 2 and common difference is 4.

Solution:

a = 2, d = 4

a₁₅ = 2 + (15-1)×4 = 58

7. How many terms are there in the A.P. 7, 11, 15, ..., 407?

Solution:

a = 7, d = 4

a + (n-1)d = 407 

= n = 101

8. Find the sum of the first 20 terms of the A.P. -3, -7, -11, -15, ...

Solution:

a = -3, d = -4, n = 20

S₂₀ = (20/2)[2(-3) + (20-1)×(-4)] 

= -820

9. Find the first term and common difference if the third term is 8 and seventh term is 20.

Solution:

a + 2d = 8

a + 6d = 20

Solving gives: a = 2, d = 3

10. If the sum of the first 7 terms of an A.P. is 91, and its first term is 2, find the common difference.

Solution:

a = 2, S₇ = 91

Solving gives: d = 11/3

11. Find the 12th term of the A.P. 2, 4, 6, 8, ...

Solution:

a = 2, d = 2

a₁₂ = 2 + (12-1)×2 = 24

12. Find the sum of the first 30 terms of the A.P. 5, 9, 13, 17, ...

Solution:

a = 5, d = 4, n = 30

S₃₀ = (30/2)[2(5) + (30-1)×4] 

= 1890

13. If the sum of the first n terms of an A.P. is 3n² + 5n, find its nth term.

Solution:

S_n = 3n² + 5n

a_n = S_n - S_n-1 = 6n + 2

14. Find the sum of the first 10 multiples of 7.

Solution:

Multiples: 7, 14, 21, ..., 70

a = 7, d = 7, n = 10

S₁₀ = (10/2)[2(7) + (10-1)×7] = 385