Question

The sum four consecutive number in an AP is 32 and the ratio of the product of the first and the last term to the product of the two middel term term is 7:5.find the number

Answer 1

Hi there!


The answer is given below :

Let, the four consecutive numbers are
(a - 3d), (a - d), (a + d) and (a + 3d).

Given that,

(a - 3d) + (a - d) + (a + d) + (a + 3d) = 32

=> 4a = 32

=> a = 8

So, the numbers will be :

(8 - 3d), (8 - d), (8 + d) and (8 + 3d).

Now,
(8 - 3d)(8 + 3d) : (8 - d)(8 + d) = 7 : 15

=> (64 - 9d²) : (64 - d²) = 7 : 15

=> (64 - 9d²)/(64 - d²) = 7/15

=> 960 - 135d² = 448 - 7d²

=> 128d² = 512

=> d² = 4

So, d = 2.

So, the numbers are :
2, 6, 10 n' 14


Hope it helps! :D

Answer 2

Look at the pic this helps you: