Question

divide 32 into 4 numbers in the AP such that the ratio of product of extreme terms to the product of middle terms is 7 ratio 15

Answer 1

lets say the 4 numbers are: a-3d, a-d, a+d, a+3d

where sum of 4 terms = 32,

hence 4a = 32, implies a = 8;

according to question:

(8-3d)(8+3d)/(8-d)(8+d) = 7/15

solving we get answer: 2,6,10,14