If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers.

Given: sum of first three terms is 24


To find: the first three terms of AP


Assume the first three terms are a - d, a, a + d where a is the first term and d is the common difference


So, sum of first three terms is a - d + a + a + d = 24


3a = 24


a = 8


given that the product of three terms is 440


so a3 - ad2 = 440


substituting a = 8


83 - 8d2 = 440


512 - 8d2 = 440


72 = 8d2


d = 3 or d = - 3


hence the given terms are a - d, a, a + d which is 5, 8, 11 or 11, 8, 5


5