Question

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Answer 1

Suppose there are n terms in the AP.

Here, a = 17, d = 9 and l = 350

$$\begin{gathered} \therefore a_n=350 \\ \Rightarrow 17+\left(n-1\right)\times 9=350\left[a_n=a+\left(n-1\right)d\right] \\ \Rightarrow 9n+8=350 \\ \Rightarrow 9n=350-8=342 \end{gathered}$$
$\Rightarrow n=38$

Thus, there are 38 terms in the AP.

$$\begin{gathered} \therefore S_{38}=\frac{38}{2}\left(17+350\right)\left[S_n=\frac{n}{2}\left(a+l\right)\right] \\ =19\times 367 \\ =6973 \end{gathered}$$

Hence, the required sum is 6973.