The second, the first and the third term of an A.P whose common difference is non zero form a G.P in that order. Find its common ratio.

Answer: -2

Explanation:

Let the terms in GP be a, ar, ar2.

Hence the terms ar, a and ar2 are in AP.

Therefore, a – ar = ar2– a

‘a’ cannot be 0. Hence, 1 – r = r2 – 1

r2 + r -2 = 0

(r + 2)(r – 1) = 0

Now r cannot be ‘1’ since common difference should be non-zero. Hence r = -2.

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