Question

The first term of an A. P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A. P.

Answer 1

We have,
$S_n$ = 1000
a = 5
l = 45

We know that,
$S_n$ = ($\frac{n}{2}$)(a+l)
[where 'n' is the number of terms]

Substitute all other values into the formula and find the value of n
$\Rightarrow$ 1000=($\frac{n}{2}$)(5+45)
$\Rightarrow$ ($\frac{1000}{50}$) = ($\frac{n}{2}$)
$\Rightarrow$ 20 = ($\frac{n}{2}$)
n = 20$\times$2
n = 40