The first and the last term 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.