Sequences and Progressions Exercise 8.3 Class 9 Maths Solutions

The Sequences and Progressions Exercise 8.3 set moves on to the Geometric Progression, or GP. These NCERT Solutions Class 9 Maths Chapter 8 Sequences and Progressions Exercise 8.3 answers show how to find the common ratio, the nth term, and a required term of a GP, with each line explained for a Class 9 student.

• Questions solved: all 7 problems of Exercise 8.3, each with clear steps.
• Main skill: use t_n = a r ^n-1 for any term of a GP.
• Chapter link: the GP rule here completes the AP and GP pair before the End-of-Chapter set.

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 8.3 Cover?

Exercise 8.3 studies the Geometric Progression. A GP multiplies each term by a fixed number, the common ratio r. You learn to find a and r, write the nth term t_n = a r ^n-1, and find which term equals a given value. One question uses a bouncing ball, and one uses the Sierpinski carpet figure, so you see how a GP models real patterns. This set is a good foundation for the Class 10 work on geometric series.

Video Walkthrough

Source: Physics Wallah Foundation on YouTube

Sequences and Progressions Exercise 8.3 Question Breakdown

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

• Q1: Find the 12th term of a GP from its 8th term and ratio.
• Q2: Find the 10th and nth terms of the GP 5, 25, 125, ...
• Q3: Build terms of a GP from a recursive rule.
• Q4: Find which term of the GP 2, 6, 18, ... is 4374.
• Q5: A bouncing-ball height problem set as a GP.
• Q6: Find which term of 2, 2√2, 4, is 128.
• Q7: The Sierpinski square carpet stages as a GP.

Sample Solved Question from Exercise 8.3

Here is Question 2 from Exercise 8.3, solved step by step, so you can see the method.

Question: Find the 10th and nth terms of the GP 5, 25, 125,

Step 1. Find the first term and the common ratio. Here a = 5 and r = 25 ÷ 5 = 5. Check: 125 ÷ 25 = 5.

Step 2. Put these into t_n = a r ^n-1: t_n = 5 × 5 ^n-1.

Step 3. Add the powers of 5: 5 × 5 ^n-1 = 5¹ × 5 ^n-1 = 5 ⁿ.

Step 4. For the 10th term, put n = 10: t₁₀ = 5¹⁰ = 9 765 625.

Final answer. The nth term is t_n = 5 ⁿ and the 10th term is 9 765 625.

How to Use These Sequences and Progressions Exercise 8.3 Solutions

Solve each GP question first, then open the Collegedunia solution to check your r and your final term. The main slip here is dividing the wrong way to find r.

• Find r by dividing a term by the one before it, never the reverse.
• Keep n-1 as the power, not n, in the nth term rule.
• Redo the ball and carpet questions to see the GP behind the story.

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.