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