The sum of three numbers in A.P. is 21 and the product of first and the third numbers exceeds the second number by 6, find the three numbers.

Let the three numbers in A.P. be a - d, a, a + d.
Since the sum of the number = 21

∴  a - d + a + a + d = 21                             or               3a = 21
or                         a = 7
Since the product of first and the third numbers exceeds the second number by 6.

∴    (a - d) (a + d) = a + 6             or           
or                      or              49 - 13 =
or                                  or                 
When d = 6, numbers are 7 - 6, 7, 7 + 6
or                                 1, 7 , 13
When d = -6, numbers are 7 + 6, 7, 7 - 6
or                                  13, 7, 1