Question

Find the four terms in ap whose sum is 8 and the sum of whose squares is 36.

Answer 1

let the nos. be (a-3d),(a-d),(a+d)and (a+3d)
now
(a-3d)+(a-d)+(a+d)+(a+3d)=8
4a=8
a=2
and
(a-3d)^2+(a-d)^2+(a+d)^2+(a+3d)^2=36
4 (a^2+5d^2)=36
(a^2+5d^2)=8
putting the value of a
4+5d^2=8
5d^2=8-4
5d^2=4
d^2=4-5
d^2=-1
d=+-1