Divide 32 into four parts which are in A.P. such that the ratio of the product of extremes to the product of means is 7:15.

Explanation

Let the four parts be (a-3d),(a-d),(a+d), and (a+3d). Then,
(a-3d)+(a-d)+(a+d)+(a+3d)=32
or 4a=32
or a=8
Also, `((a-3d)(a+3d))/((a-d)(a+d))=7/15`
or `(a^(2)-9d^(2))/(a^(2)-d^(2))=7/15`
or `(64-9d^(2))/(a^(2)-d^(2))=7/15`
or `128d^(2)=512`
or `d^(2)=4`
or `d=pm2`
Thus, the four parts are 2,6,10,14.