Question

Find three numbers in AP whose sum is 15 and product is 80.

Answer 1

Let the required numbers be (a - d), a and (a + d).
Then (a - d) + a + (a + d) = 15
⇒ 3a = 15
⇒ a = 5​
Also, (a - d).a.(a + d)​ = 80
⇒ a(a² - d²) = 80​
⇒ 5 ​(25 - d²) = 80​ ​
⇒ d² = 25​ - 16 = 9
⇒ d = $\pm$3
Thus, a = 5 and d = $\pm$3
Hence, the required numbers are (2, 5 and 8) or ( 8, 5 and 2).