Writing x = ar³, y = ar⁹ and z = ar¹⁵, we compute y² = (ar⁹)² = a²r¹⁸. Also x x z = (ar³) x (ar¹⁵) = a²r¹⁸. Since y² = x x z, x, y, z form a GP.
If the 4th, 10th and 16th terms of a GP are x, y and z respectively, prove that x, y, z are in GP.
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Let the GP have first term a and common ratio r.
Given:
4th term: x = ar³
10th term: y = ar⁹
16th term: z = ar¹⁵
Now check the square of the middle term:
y² = (ar⁹)² = a²r¹⁸.
Now calculate the product of the first and third terms:
x x z = (ar³) x (ar¹⁵) = a² x r³⁺¹⁵ = a²r¹⁸.
Since y² = x x z, the ratio y / x equals z / y = r⁶.
Therefore, x, y and z are in GP.
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/