Q12 of 176 Page 21

If 5^th, 8^th and 11^th terms of a G.P. are p, q and s respectively, prove that a² = ps.

T_n = ar^n-1

According to the question,

⇒ T₅ = a.r⁴

⇒ T₈ = a.r⁷

⇒ T₁₁ = a.r¹⁰

To Prove: q²=p.s

⇒ T₅ = a.r⁴ = p

⇒ T₈ = a.r⁷ = q

⇒ T₁₁ = a.r¹⁰=s

q²= (a.r⁷)² = a².r¹⁴…(1)

p.s = (a.r⁴)(a.r¹⁰) = a².r¹⁴…(2)

∴ from (1) and (2) we get

⇒ q²=p.s

Hence, Proved.

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If 5th, 8th and 11th terms of a G.P. are p, q and s respectively, prove that a2 = ps.