Question

divide 32 into 4 parts which are the four terms of ap such that product of first and the fourth term is to the product of second and third terms as 7:15​

Answer 1

Answer:

2,6,10,14

Step-by-step explanation:

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−3d)(a+3d). 7

__________ = ___

(a−d)(a+d). 15

⟹a ^2−9d^2. 7

_________. =_____

a ^2−d^2. 15

64−9d^2. 7

_________. =_____

64−d^2. 15

⟹128d^2=512

⟹d^2=4

⟹d=±2

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