Question

find the answer of given question

Answer 1

Answer:

2,6,10,14

Step-by-step explanation:

Let (a-3d),(a-d),(a+d)and(a+3d) are four consecutive numbers in an A.P.

Given,

Sum of four consecutive numbers in an AP is 32

=> a - 3d + a - d + a + d + a + 3d = 32

=> 4a = 32

=> a = 32/4

=> a = 8.

Ratio of the product of the first and the the last term to the middle most term is 7:15

(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

=> 64 = 128d²

=> d = ±2

When a = 8, d = +2:

a - 3d = 2

a + 3d = 14

a - d = 6

a + d = 10

When a = 8, d = -2:

a - 3d = 14

a + 3d = 2

a - d = 10

a + d = 6

Series is 2,6,10,14.

Hope it helps!