Question
Sat February 23, 2008 By:

Divide 32 into 4 parts such that all are in A.P such that the ratio of product of extremes to the p

Expert Reply
Arun
Sat February 23, 2008

Your question was 
Divide 32 into 4 parts such that all are in A.P such that the ratio of product of extremes to the product of means is 7: 15.

Let us take the 4 numbers in AP as a-3d,a-d,a+d,a+3d

Now a-3d+a-d+a+d+a+3d = 32
So 4a = 32
a = 8
Also According to II condition

(a2 -9d2):(a2-d2) =7:15

So 15( a2 -9d2) = 7(a2-d2)
15(64 - 9d2) = 7(64-d2)

Solving we get d = 2

So the AP is 2,6,10,14 or 14,10,6,2

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