Representing terms as a/r, a, ar gives product a³ = -1, so a = -1. Using sum -1/r – 1 – r = 13/12 gives common ratio r = -3/4 or -4/3, yielding terms 4/3, -1, 3/4 or 3/4, -1, 4/3.
The sum of the first three terms of a GP is 13/12 and their product is –1. Find the common ratio and the terms.
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Let the three terms be a/r, a and ar.
Their product is:
(a/r) x a x ar = -1
a³ = -1, which gives a = -1.
Their sum is 13/12:
-1/r – 1 – r = 13/12
-(1/r + r) = 13/12 + 1 = 25/12
(r² + 1) / r = -25/12
12r² + 25r + 12 = 0
(3r + 4)(4r + 3) = 0.
So r = -4/3 or r = -3/4.
When r = -4/3, terms are: 3/4, -1, 4/3.
When r = -3/4, terms are: 4/3, -1, 3/4.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 8 Predicting What Comes Next: Exploring Sequences and Progressions Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-8/