Question

The sum of three numbers in AP is 3 their product is −35. Find the numbers.

Answer 1

Let the required numbers be (a - d), a and (a + d).
Then (a - d) + a + (a + d) = 3
⇒ 3a = 3
⇒ a = 1​
Also, (a - d).a.(a + d)​ = -35
⇒ a(a² - d²) = -35​
⇒ 1​.​(1​ - d²) = -35​ ​ ​
⇒ d² = 36
⇒ d = $\pm$6

Thus, a = 1 and d = $\pm$6
Hence, the required numbers are ( -5, 1 and 7) or ( 7, 1 and -5).