Question

Question 3 The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.

Class X1 - Maths -Sequences and Series Page 192

Answer 1

Let ,
a is the first term.
d is the common ratio of GP.
we know,
Tₙ = arⁿ⁻¹ use it here,
Given,
T₅ = P
ar⁵⁻¹ = ar⁴ = P -------------(1)

T₈ = q
ar⁸⁻¹ = ar⁷ = q-----------------(2)

T₁₁ = s
ar¹¹⁻¹ = ar¹⁰ = s -----------------(3)

now multiplying equations (1)and (3)
ar¹⁰ × ar⁴ = Ps
a² × r¹⁴ = Ps
(ar⁷)² = Ps
from equation (1)

(q)² = Ps
q² = Ps
hence proved

Answer 2

I hope it will help u