Thread: Arithmetic progression and ratio of terms.

Divide 32 into 4 parts which are in AP such that the ratio of the product of the extremes to the product of the means is 7:5 .

If I'm interpreting your problem correctly, something is wrong in your problem.

Consider the sequence:

a-3d,a-d,a+d,a+3d

This is an arithmetic progression with constant difference 2d.

The product of the 2 outer terms is a^2 - 9d^2. The product of the 2 inner terms is a^2 - d^2.

Your requested ratio is:


which leads to


which is impossible.

But I got this problem in my exam

Hello, prantik007!

Please check the problem for typos.
As stated, the situation is patently impossible.

Divide 32 into 4 parts which are in AP such that the ratio of the product
of the extremes to the product of the means is 7:5 .??

The four parts are: .

The product of the extremes is: .

The product of the means is: .

. . It is obvious that: .


So how can . ?