Question

The first and the last term 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

Find the number of terms and their sum

First-term, $a=17$

Last term, $l=350$

Common difference, $d=9$

Let there be $n$ terms in the A.P., thus the formula for the last term can be written as;

$$\begin{gathered} l=a+(n-1)d \\ 350=17+(n-1)9 \\ 333=(n-1)9 \\ (n-1)=37 \\ n=38 \\ {S}_n=\frac{n}{2}(a+l) \\ {S}_{38}=\frac{38}{2}\times (17+350) \\ =19\times 367 \\ =6973 \end{gathered}$$

Hence, this A.P. contains $38$ terms and the sum of the terms of this A.P. is $6973.$