Question

# Sum of first 12 terms of a GP is equal to the sum of the first 14 terms in the same GP. Sum of the first 17 terms is 92, what is the third term in the GP

Correct option is

**Explanatory Answer :**

Sum of first 14 terms = Sum of first 12 terms + 13th term + 14th term

Sum of first 12 terms is equal to sum of first 14 terms.

=> Sum of first 12 terms = Sum of first 12 terms + 13th term + 14th term

It is when possible then 13th term + 14th term = 0

Suppose 13th term = k, common ratio = r. 14th term will be k r.

k + k r = 0

k (1 + r) = 0

=> r = -1 as k cannot be zero

Common ratio = -1.

Now, if the first term of this GP is a, second term would be -a, third would be a and so on

The GP would be a, -a, a, -a, a, -a,...

Sum to even number of terms = 0

Sum to odd number of terms = a

Here, sum of the first 17 terms = 92

=> a = 92

Third term = a = 92

so , A is the corect option