The sum of three numbers in A.P. is -3 and the product is 8. Find the numbers.

Let the three numbers in A.P. be a - d, a, a + d.

Given, S_n = -3

⇒ a - d + a + a + d = -3
⇒ 3a = -3
⇒ a = -1.

Given, product of numbers = 8

⇒ (a - d)a(a + d) = 8

Putting value of a = -1

⇒ (-1 - d)(-1)(-1 + d) = 8
⇒ (d + 1)(d - 1) = 8
⇒ d² - 1 = 8
⇒ d² = 9
⇒ d = -3, 3.

Putting d = -3
Numbers ⇒ a - d = -1 - (-3) = -1 + 3 = 2, a = -1, a + d = -1 + (-3) = -4.

Putting d = 3
Numbers ⇒ a - d = -1 - 3 = -4, a = -1, a + d = -1 + 3 = 2.

Hence, the three numbers in A.P. are -4, -1, 2 or 2, -1, -4.