Question

find the four consecutive term in ap whose sum is 72 and the ratio of product of the extremes to the product of the mean 9:10

Answer 1

a-2d,a-d,a,a+d
sum = 4a -2d =72
(a-2d)(a+d)/(a-d)(a) = 9/10
10 (a2-ad -2d2) = 9(a2- ad)
a2 -ad -20d2 = 0
a2- 5ad +4 ad - 20d2 = 0
(a-5d)(a+4d) = 0
a = 5d
18d =72
d = 4
a = 20
12,16,20,24
Please comment if you have any doubt