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 .

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- March 8th 2010, 10:24 PMprantik007Arithmetic 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 .

- March 9th 2010, 09:26 AMqmech
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. - March 9th 2010, 07:23 PMprantik007
But I got this problem in my exam

- March 10th 2010, 11:19 AMSoroban
Hello, prantik007!

Please check the problem for typos.

As stated, the situation is patently impossible.

Quote:

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 isthat: .*obvious*

So how can . ?