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If the p^th, q^th and r^th terms of an A.P are in GP, then the common ratio of the G.P is

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If the pth, qth and rth terms of an A.P are in GP, then the common ratio of the G.P is

(a)  p + q/r + q

(b)  r - q/q - p

(c)  p - r/p - q

(d)  None of these

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1 Answer

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Best answer

Correct option (b)  r – q/q – p

Explanation:

Tp , Tq , Tr are in G.P

⇒ Tq/Tp  = Tr/Tq ⇒   Tq/Tp - 1 = Tr/Tq - 1

⇒ Tq/Tp/Tp = Tr/Tq /Tq 

∴ Tq/Tp = Tr - Tq/Tq - Tp

⇒ Tq/Tp  = (A (r –1)D) – (A (q – 1)D)/(A (q –1)D) – (A (p – 1)D)

= r - q/q - p

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