Question

The fifth, eight and eleventh terms of a geometric progression are p, q and r respectively. Show that : q² = pr.

Answer 1

Let the first term of the G.P. be a and its common ratio be r.

5^th term = t₅ = p

`=>` ar⁴ = p

8^th term = t₈ = q

`=>` ar⁷ = q

11^th term = t₁₁ = r

`=>` ar¹⁰ = r

Now,

pr = ar⁴ × ar¹⁰

= a² × r¹⁴

= (a × r⁷)²

= q²

`=>` q² = pr