Question

If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are ______.

Options

• 2, 4, 6

• 1, 5, 3

• 2, 8, 4

• 2, 3, 4

Answer 1

If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are 2, 3, 4.

Explanation:-

Let three numbers be a - d, a, a + d

∴ a - d +a + a + d = 9

⇒ 3a = 9

⇒ a = 3

Also

(a - d) × a × (a + d) = 24

⇒ (3 - d) × 3(3 + d) = 24

⇒ 9 - d² = 8

⇒ d² = 9 - 8 = 1

∴ d = ± 1

Hence numbers are 2, 3, 4 or 4, 3, 2