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