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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

A
B
C
D
##### 231
Solution

Correct option is

(A)

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