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Q35 of 74 Page 9

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

Let a and r be the first term and common ratio respectively.

5^th term = a₅ = ar⁴
p = ar⁴

a₈ = ar⁷

q = ar⁷

a₁₁ = ar¹⁰

s = ar¹⁰

q² = (ar⁷)²= a² r¹⁴

ps = ar⁴ ar¹⁰= a²r⁴⁺¹⁰= a² r¹⁴

∴ q² = ps

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