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

Answer:

Given,

Sum of first three terms is 24

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

Sum of first three terms is a – d + a + a + d = 24

3a = 24

a = 8

It is given that the product of three terms is 440

So a³ – ad² = 440

Substitute the value of 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