Question

The first and last terms of an AP are 4 and 81 respectively. If the common difference is 7, how many terms are there in the AP and what is thir sum ?

Answer 1

Here, a = 4, d = 7 and l = 81

Let its n^th term be 81.
Then T_n = 81
⇒a + (n-1) d = 81

⇒ 4 + ( n -1​) ⨯​ 7 = 81
⇒ 7n = 84
⇒ n = 12
Hence, there are 12 terms in the AP.

∴ S_n = $\frac{n}{2}\left(a+l\right)$
$=\left(\frac{12}{2}\right)\times \left(4+81\right)=6\times 85=510$
Hence, the required sum is 510.