Question

In an AP the first term is 2, the last term is 29 and sum of all the terms is 155. Find the common difference of the AP.

Answer 1

Here, a = 2, l = 29 and S_n = 155
Let d be the common difference of the given AP and n be the total number of terms.
Then T_n = 29
⇒ a + (n - 1)d = 29
⇒ 2 + (n - 1)d = 29​ ...(i)

The sum of n terms of an AP is given by
$$\begin{gathered} S_n=\frac{n}{2}\left[a+l\right]=155 \\ \Rightarrow \frac{n}{2}\left[2+29\right]=\left(\frac{n}{2}\right)\times 31=155 \\ \Rightarrow n=10 \end{gathered}$$
Putting the value of n in (i), we get:
⇒ 2 + 9d = 29
⇒ 9d = 27
⇒ d = 3
Thus, the common difference of the given AP is 3.