Divide 56 in four parts in AP such that the ratio of the product of their extremes
(1st and 4th) to the product of means (2nd and 3rd) is 5:6.
#Answer.
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Let the four parts be a−3d,a−d,a+d,a+3d
Sum, 4a=56
a=14
(a−d)(a+d)
(a−3d)(a+3d)
=
6
5
6(a
2
−9d
2
)=5(a
2
−d
2
)
a
2
=49d
2
d=±2
For d=2,
Numbers are 8,12,16,20.
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Answer:
Divide 56 in four parts in AP, such that the ratio of the product of extremes to the product of means is 5:6. ... The sum of the terms of the A.P is 56, and the ratio of the product of extremes to the product of the means is 5:6.
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