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Question

The sum of three numbers in AP is 27 and their product is 405. Find the numbers.

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Solution

Let the required numbers be (a - d), a and (a + d).
Then (a - d) + a + (a + d) = 27
⇒ 3a = 27
⇒ a = 9​
Also, (a - d).a.(a + d)​ = 405
⇒ a(a2 - d2) = 405​
9​(81​​ - d2) = 405​ ​ ​
d2 = 81​​ - 45 = 36
d = ±6
Thus, a = 9 and d = ±6
Hence, the required numbers are (3, 9 and 15) or (15, 9 and 3).

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