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

Explanation

Let the our parts are `a-3d,a-d,a+d and a+3d`.

Then by the given question,

`a-3d+a-d+a+d+a+3d=32`
or, `4a=32`

or, `a=8` and

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

or,` a²-9d²/a²-d²=7/15`

or, `15a²-135d²=7a²-7d²`

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