Question

The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.

Answer 1

Given,
a = 2
l = 50
$\therefore$ l = a + (n - 1)d
50 = 2 + (n - 1)d
(n - 1)d = 48 ....(i)
$S_n$ of all n terms is given 442
$\therefore S_n=\frac{n}{2}[a+l]442=\frac{n}{2}[2+50]$
Or n = 17 ...... (ii)
From (i) and (ii)
$d=\frac{48}{n-1}=\frac{48}{16}=3$
The common difference is 3.