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