Question

There are four numbers in A.P. Their sum is 20 and sum of their squares is 120. Find largest of those numbers?

Answer 1

Let the four numbers in A.P be $a-3d,a-d,a+d,a+3d$

$Sum=4a=20$
$a=5$ Sum of their squares $=a^2-6ad+9d^2+a^2-2ad+d^2+a^2+6ad+9d^2+a^2+2ad+d^2=4a^2+20d^2=120$
$20d^2=120-4\times 25=20$
$d^2=1$ or $d=\pm 1$
Hence the numbers are $2,4,6,8$ or $8,6,4,2$.