Divide 32 into 4 parts which are in ap

Asked by admin @ 11/08/2021 in Math viewed by 335 People

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.

Answered by admin @ 11/08/2021

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
or, 15a²-7a²=-7d²+135d²
or, 8a²=128d²
or, 8×8²=128d²
or, d²=8×8×8/128
or, d²=4
or, d=+-2
∴, The four parts are:
when d=2
8-(3×2)=8-6=2
8-2=6
8+2=10
8+(3×2)=14
when d=-2
8-(3×-2)=8+6=14
8-(-2)=8+2=10
8+(-2)=8-2=6
8+(3×-2)=8-6=2

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