Question

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

Answer 1

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 = $\pm$6
Thus, a = 9 and d = $\pm$6
Hence, the required numbers are (3, 9 and 15) or (15, 9 and 3).