Question

If the sum of n terms of an A.P. is 2n² + 5n and its mth term is 164, find the value of m.

Answer 1

Let a and b be the first term and the common difference of the A.P. respectively.

Comparing the coefficient of n² on both sides, we obtain

Comparing the coefficient of n on both sides, we obtain

Therefore, from (1), we obtain
8 + (m – 1) 6 = 164
⇒ (m – 1) 6 = 164 – 8 = 156
⇒ m – 1 = 26
⇒ m = 27
Thus, the value of m is 27.