Find four numbers in A.P. whose sum is 32 and the product of extremes is to the product of means is 7 : 15.

Let the four number in A.P. be a - 3d, a - d, a + d, a + 3d.
Since the sum of four numbers  = 32

∴   a - 3d + a - d + a + d + a + 3d = 32
or                               4a = 32                         or                 a = 8
Since the ratio of the product of extremes to the product of means is 7:15.

∴                  or                
or                           or            
or             or            
or                                       or                     
When d = 2 and a = 8 numbers are 8 - 3(2), 8 - 2, 8 + 2, 8 + 3(2)
                              2, 6, 10, 14
When d = -2 and a = 8 numbers are 8 - 3(-2), 8 - (-2), 8 + (-2), 8 + 3(-2)
                               14, 10, 6, 2