Sum of first 12 terms is equal to sum of first 14 terms.
Sum of first 14 terms = Sum of first 12 terms + 13^{th} term + 14^{th} term
=> 13^{th} term + 14^{th} term = 0
Let us assume 13^{th} term = k, common ratio = r. 14^{th} term will be kr.
k + kr = 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
Sum to 17 terms is 92 => a = 92
Third term = a = 92
Correct Answer: 92
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