divide 32 into 4 parts which are in A.P.such that the product of extremes is to the product of means is 7:15.
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lets say the 4 numbers are: a-3d, a-d, a+d,
a+3d
where sum of 4 terms = 32
a-3d+a-d+a+d+a+3d=32
4a = 32
a = 8
a/q
(8-3d)(8+3d)/(8-d)(8+d) = 7/15
64-9d^2
------------ = 7/15
64-d^2
960-135d^2=448-7d^2
-128d^2= -512
d^2=4
d=2
these terms are 2,6,10,14
a+3d
where sum of 4 terms = 32
a-3d+a-d+a+d+a+3d=32
4a = 32
a = 8
a/q
(8-3d)(8+3d)/(8-d)(8+d) = 7/15
64-9d^2
------------ = 7/15
64-d^2
960-135d^2=448-7d^2
-128d^2= -512
d^2=4
d=2
these terms are 2,6,10,14
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