Question

The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Answer 1

Given that, $a = 5$, $l = 45$ and $S_n = 400$
$S_n = \frac n2(a+l)$

$400 = \frac n2(5+45)$

$400 = \frac n2(50)$

$\frac { 400 \times 2}{50} = n$

$n = 16$
$l = a + (n−1)d$
$45 = 5 + (16 − 1) d$
$40 = 15d$

$d = \frac {40}{15}$

$d = \frac {8}{3}$