Question

The sum of three consecutive terms of an A.P. is 36 and their product is 1140.

Find the terms. (Consider the terms to be in descending order.)​

Answer 1

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Answer 2

Step-by-step explanation:

Given The sum of three consecutive terms of an A.P. is 36 and their product is 1140.  Find the terms. (Consider the terms to be in descending order.)​

• Let  x + d, x, x - d be the three terms of  an A.P.
• Given sum of these terms is 36. So we have
•     x + d + x + x - d = 36
•            3x = 36
•              x = 36 / 3
•              x = 12
• Now according to question product of these terms is 1140
• So we have x = 12, substituting we get
•         (12 + d) (12) (12 - d) = 1140
•          (12 + d) (12 – d) (12) = 1140
•              12^2 – d^2 = 1140 / 12 (since (a + b)(a – b) = a^2 – b^2)
•              144 – d^2 = 95
•                144 – 95 = d^2
•                    d^2 = 49
•                    d = √49
•                     d = 7
• Therefore the three terms are 12 + 7, 12, 12 - 7
•                                                = 19, 12, 5 .

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