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Question -

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



Answer -

Given:

Sum of first threeterms is 24

Let us assume thefirst three terms are a – d, a, a + d [where a is the first term and d is thecommon difference]

So, sum of first threeterms is a – d + a + a + d = 24

3a = 24

a = 8

It is given that theproduct of three terms is 440

So a3 –ad2 = 440

Substitute the valueof a = 8, we get

83 –8d2 = 440

512 – 8d2 =440

72 = 8d2

d = 3 or d = – 3

Hence, the given termsare a – d, a, a + d which is 5, 8, 11

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