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.