Answer :

Let 32 be divided into parts as (a - 3d), (a - d), (a + d) and (a + 3d).

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

4a = 32

a = 8

Now, we are given that product of the first and the fourth terms is to the product of the second and the third terms as 7 : 15.

i.e. [(a - 3d) × (a + 3 d)] : [(a - d) × (a + d)] = 7 : 15

=

15[(a - 3d) × (a + 3 d)] = 7[(a - d) × (a + d)]

15[a2 - 9d2] = 7 [a2 - d2]

15a2 - 135d2 = 7a2 - 7d2

8a2 - 128d2 = 0

8a2 = 128d2

Putting the value of a, we get,

512 = 128 d2

d2 = 4

d =  ±2

If d = 2, then the numbers are 2, 6, 10, 14.

If d = - 2, then the numbers are 14, 10, 6, 2.

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