Question

solve this question with method

Answer 1

Let the four terms in A.P be
a - 3d , a-d , a+d and a+3d.

Now, 
a - 3d + a - d + a +d + a + 3d = 32
∴  4a = 32
∴ a = 8

Now,
The terms at the extremes are ( a - 3d ) and ( a + 3d )
and the middle terms are a- d & a+d

∴ a-3d*a+3d / a-d * a+d = 7/15
∴ a² - 9d² / a² - d² = 7/15
∴ 15 ( a² - 9d² ) = 7 ( a² - d² )
∴ 15a² - 135d² = 7a² - 7d²
∴ 8a² = 128d²
∴ a² = 16d²
∴ 8² = 16d²
∴ d² = 64/16
∴ d² = 4
∴ d = +- 2

Now, the four terms are a-3d = 8-6 = 2,
a -d = 8-2 = 6 
a + d = 8+2 = 10 
& a + 3d = 8+6 = 14

∴ The four numbers are 2,6,10 and 14.