Question

Divide 56 in four parts in AP such that ratio of product of the extremes to the product of their means is 5:6. Find the numbers.

Answer 1

You cannnot take a-2d and a+2d in place of a-3d and a+3d. Because then it will not be an AP.

Explanation:
if we take like that, the series will be;
a-2d, a-d, a+d, a+2d
here difference between first 2 terms is = d
difference between 2nd and 3rd = 2d
so in AP, difference between any terms should be equal (common difference).

now if take a-2d,a-d,a,a+d then it is ok. But it will increase the steps. Because the sum of all four terms will contain both 'a' and 'd' terms. But in above case only 'a' term is present and we easily got the first term from the equation(ie; a = 14).

Hope you understand.