Question

I took terms as a-2d ,and,a+d and a+2d is the answer will be crrct

Answer 1

Look at the pic nd u will get the right answer

Answer 2

The answer is given below :

Since a-2d, a-d, a+d and a+2d are considered by you as terms of AP.

2nd term - 1st term
= a - d - a + 2d = d,

3rd term - 2nd term
= a + d - a + d = 2d

and

4th term - 3rd term
= a + 2d - a - d = d.

We are getting two different common difference d and 2d, which is not possible for an AP.

The correct terms are

a - 3d, a - d, a + d and a + 2d,
where 2d is the common difference.

Sorry that your assumption was wrong.

♧

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 are

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

Given that :

(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, 14

or,

14, 10, 6, 2.

Therefore, the four consecutive numbers are

2, 6, 10, 14.

Thank you for your question.