Question

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. ​

Answer 1

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.

Answer 2

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.