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

**Given: **

The first and the last terms of an A.P. are 17 and 350 respectively and the common difference $d=9$.

**To do: **

We have to find the numbers of the terms in the given A.P. and the sum of the terms.

**Solution:**

Let the first term of the given A.P. be $a$, common difference $d$, the last term $l$ and the number of terms $n$.

We know that,

$l=a+( n-1) d$

On substituting $l=350,\ a=17\ and\ d=9$, we get,

$350=17+( n-1)9$

$\Rightarrow n-1=\frac{350-17}{9}={333}{9}=37$

$\Rightarrow n=37+1=38$

The sum of $n$ terms in an A.P. $S_{n}=\frac{n}{2} \ ( a+l)$

$=\frac{38}{2}( 17+350)$

$=19(367)$

$=6973$

**Hence, the given A.P. has 38 terms and the sum of its terms is 6973.**

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