Question

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and last term to the product of two middle terms is 7:15 . Find the numbers.

Answer 1

let the four numbers which are in ap be
a-3d,a-d,a+d,a+3d
given sum of these terms=32
then, a-3d+a-d+a+d+a+3d=32
                    4a=32
                        a=32/2
                         a=8
they had given that,
the ratio of the product of the first and last term to the product of middle term =7:15
(a-3d)(a+3d)/(a-d)(a+d)=7/15
15a^2-135d^2=7a^2-7d^2
a=8
d^2=512-128
d^2=4
d=2 or -2