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 their sum?

Answer 1

Here, a = 4, d = 7 and l = 81
Let the n^th term be 81.
Then T_n = 81
⇒ a + (n - 1)d = 4 + (n - 1)7 = 81
⇒ (n - 1)7 = 77
⇒ (n - 1) = 11
⇒ n = 12
Thus, there are 12 terms in the AP.

The sum of n terms of an AP is given by
$$\begin{gathered} S_n=\frac{n}{2}\left[a+l\right] \\ \therefore S_{12}=\frac{12}{2}\left[4+81\right]=6\times 85=510 \end{gathered}$$

Thus, the required sum is 510.