Question

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

Answer 1

Let a and d are the first term and the common difference for an AP respectively.
Number of terms of AP = n
Last term = nth term = l = $a_n$
a = 17 , d = 9 ,
l = 350
a + ( n - 1 ) d = 350
$\Rightarrow$17 + ( n - 1 ) 9 = 350
$\Rightarrow$( n - 1 ) 9 = 350 - 17
$\Rightarrow$( n - 1 ) 9 = 333
$\Rightarrow$n - 1 = $\frac{333}{9}$
$\Rightarrow$n - 1 = 37
$\Rightarrow$n = 37 + 1
$\Rightarrow$n = 38
Therefore,number of terms in given AP = n = 38
Sum of n terms of AP = $S_n$

$S_n$ = ( a + l )
Here, n= 38
$\Rightarrow$$S_{38}$ = 19[ 17 + 350 ]
$\Rightarrow$$S_{38}$ = 19 × 367
$\Rightarrow$$S_{38}$ = 6973