Question

The sum of 4 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 term is 7:15 . Find the numbers

Answer 1

The sum of 4 consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of the middle terms is 7:15. find the numbers.

Answer 2

Let the four consecutive numbers in AP be a-3d,a-d,a+d,a+3d.

So,

        a-3d+a-d+a+d+a+3d=32

        4a=32

        a=8 

        (a-3d)(a=3d) / (a-d)(a+d)=7/15

        15(a^2-9d^2) = 7(a^2-d^2)

         15a^2-135d^2 = 7a^2-7d^2

          8a^2-128d^2 = 0

          d^2 = 4, 

             d=±2