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Question -

Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers



Answer -

Given:

Sum of first threeterms is 27

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

So, sum of first threeterms is

a тАУ d + a + a + d = 27

3a = 27

a = 9

It is given that theproduct of three terms is 648

So, a3 тАУad2 = 648

Substituting the valueof a = 9, we get

93 тАУ9d2 = 648

729 тАУ 9d2 =648

81 = 9d2

d = 3 or d = тАУ 3

Hence, the given termsare a тАУ d, a, a + d which is 6, 9, 12.

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