The sum of the first 10 terms of a GP is equal to the sum of the first 12 terms in the same GP. The sum of the first 17 terms is 42, what is the fourth term in the GP?

The sum of the first 10 terms of a GP is equal to the sum of the first 12 terms in the same GP. The sum of the first 17 terms is 42, what is the fourth term in the GP? Correct Answer –42

Sum of first 10 terms is equal to sum of first 12 terms.

Sum of first 10 terms = Sum of first 10 terms + 11^th term + 12^th term

11^th term + 12^th term = 0

Let 11^th term = k,

Common ratio = r

12^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, the 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 42