Sequences and Progressions Exercise 8.2 Class 9 Maths Solutions

The Sequences and Progressions Exercise 8.2 set is all about the Arithmetic Progression, or AP. These NCERT Solutions Class 9 Maths Chapter 8 Sequences and Progressions Exercise 8.2 answers show how to find the nth term, the common difference, and simple sums, with every line written out for a Class 9 student.

• Questions solved: all 7 problems of Exercise 8.2, each with clear steps.
• Main skill: use t_n = a + (n-1)d for any term of an AP.
• Chapter link: the AP rule here leads straight into GP work in Exercise 8.3.

These solutions are prepared by subject teachers, matched to the current 2026-27 NCERT, and checked step by step so a Class 9 student can follow each line.

What Does Class 9 Maths Chapter 8 Sequences and Progressions Exercise 8.2 Cover?

Exercise 8.2 studies the Arithmetic Progression. An AP adds a fixed number, the common difference d, to each term. You learn to spot a and d, write the nth term t_n = a + (n-1)d, and find a required term. Some questions use two known terms to find the AP, and a few bring in short word problems on salary and marbles. This set is a common source of scoring questions in the Class 9 annual exam.

Video Walkthrough

Source: Physics Wallah Foundation on YouTube

Sequences and Progressions Exercise 8.2 Question Breakdown

The exercise has 7 questions. The list below shows what each one asks.

• Q1: Find the 10th and 26th terms of the AP 3, 8, 13, 18, ...
• Q2: Find which term of an AP is -81, and if 0 is a term.
• Q3: Find the nth term and recursive rule of a falling AP.
• Q4: Use the 3rd term and last term of a 50-term AP.
• Q5: Count 2-digit numbers divisible by 3 and add them.
• Q6: A salary word problem set as an AP.
• Q7: Marbles arranged in rows, one more each row.

Sample Solved Question from Exercise 8.2

Here is Question 3 from Exercise 8.2, solved step by step, so you can see the method.

Question: Find the nth term of the AP 11, 8, 5, 2, and write its recursive rule.

Step 1. Find the first term and the common difference. Here a = 11 and d = 8 - 11 = -3. Check: 5 - 8 = -3 and 2 - 5 = -3.

Step 2. Put these into t_n = a + (n-1)d: t_n = 11 + (n-1)(-3).

Step 3. Simplify: t_n = 11 - 3n + 3 = 14 - 3n. Check: t₄ = 14 - 12 = 2, which matches the list.

Step 4. Write the recursive rule. Start at t₁ = 11, and take 3 off each time: t_n+1 = t_n - 3.

Final answer. The explicit rule is t_n = 14 - 3n, and the recursive rule is t₁ = 11, t_n+1 = t_n - 3.

How to Use These Sequences and Progressions Exercise 8.2 Solutions

Solve each AP question yourself, then use the Collegedunia solution to confirm your a, d, and final term. Small sign errors are the main marks lost here.

• Write a and d at the top before you use any formula.
• Always check one known term at the end to catch a wrong d.
• Redo the word problems once more, since they need careful reading.

More Class 9 Maths Sequences and Progressions Solutions

Use the table below to open the full chapter page or any other exercise of this chapter.