Question

16:9:28:12
find the product or extreme and product of means and hand show that the following are in​

Answer 1

Answer:

Let the four parts be (a−3d),(a−d),(a+d) and (a+3d).

Then, Sum of the numbers =32

⟹(a−3d)+(a−d)+(a+d)+(a+3d)=32⟹4a=32⟹a=8

It is given that

(a−d)(a+d)

(a−3d)(a+3d)

=

15

7

⟹

a

2

−d

2

a

2

−9d

2

=

15

7

⟹

64−d

2

64−9d

2

=

15

7

⟹128d

2

=512⟹d

2

=4⟹d=±2

Thus, the four parts are a−3d,a−d,a+d and 3d, i.e. 2,6,10,14.