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

1.	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 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.

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

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.