Question

Find the numbers of ap whose sum is 15 and sum of whose square is 83

Answer 1

let a-d,a,a+d are the three parts which are in Ap

→given a-d+a+a+d=15

→3a=15

→a=5

now, sum of their squares is 83

→(a-d)²+a²+(a+d)²=83

→a²+d²+a²+a²+d²=83

→3a²+2d²=83

→3(25)+2d²=83

→75+2d²=83

→2d²=8

d²=4

d=±2

then the numbers will be 3,5,7

the least value is 3