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nth term of Geometric Sequence
Last updated at June 9, 2026 by Teachoo
Class 9
Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress
- Definition
- Explicit Rule for a Sequence
- Recursive Rule for a Sequence
- Virahānka–Fibonacci sequence
- Exercise Set 8.1
- Arithmetic Progressions
- Visualising an AP
- Sum of the First n Natural Numbers
- Exercise Set 8.2
-
Geometric Progressions
- Fractals as a GP Sequence
- Visualising a GP
- Exercise Set 8.3
- End-of-Chapter Exercises
Transcript
nth term of Geometric SequenceFor GP Here, nth term = arn−1 The 3rd term is a3 = ar3−1 = ar2 = 1 × 22 = 4 The 7th term is a7 = ar7−1 = ar6 = 1 × 26 = 64 Let’s do an example Find the 10th and nth terms of the G.P. 5, 25,125,… . 5, 25,125,… Here, First term = a = 5 , Common ratio = r = 𝟐𝟓/𝟓 = 5 We know that nth term of a GP is an = arn – 1 Now, nth term of GP = an = arn–1 Putting values = 5 × (5)n–1 = 51 × 5n – 1 = 51 + n – 1 = 5n Hence, nth term of G.P. = 5n For 10th term of GP Putting n = 10 in an an = 5n a10 = 510 Hence, nth term of GP is 5n & 10th term of GP is 510
