Question

Sum of four consecutive numbers in ap is 20 . And the ratio of the product of the first and last term to the product of two middle term is 2:3 . Find the numbers

Answer 1

Step-by-step explanation:

given,

sum of 4 terms in A. P =20

ratio of product of extremes to means = 2:3

let the terms be

(a-3d) ,(a-d), (a+d) and (a+3d)

sum of terms is 20

4a = 20

a is 5

ratio of extremes to means =2:3

((a-3d)(a+3d))/(a+d)(a-d) = 2:3

(a²-9d²)/a²-d² = 2:3

3(a²-9d²) = 2(a²-d²)

3a²-27d²=2a²-2d²

a²=25d²

substitute a as 5

5²=25d²

d²=1

d = ±1

if d is +1

then terms are 2,4,6,8

if d is -1

then the terms are 8,6,4,2