Question

divide 32 into 4 parts which are the four terms of an ap such that the ratio of product of the first and fourth term is 2 the product of second hand for term as 7 ratio 32​

Answer 1

let the numbers be a-3d,a-d,a+d,a+3d

so,

a-3d+a-d+a+d+a+3d=32

4a=32

a=8

given,

the product of first term and fourth term = (a+3d)(a-3d)=a^2-(3d)^2

=a^2-9d^2

the product of second term and third term =(a-d()(a+d)=a^2-d^2

now

(a^2-9d^2)/(a^2-d^2)=7/32

32a^2-288d^2=7a^2-7d^2

25a^2=281d^2

25(64)=281d^2

d^2=5.7

Answer 2

Refers to attachment ⚘⚘