Question

13. The sum of three numbers in AP is -3 and the product is 8. Find the numbers​

Answer 1

Let the 3 numbers in A.P be:

• (a - d)
• (a)
• (a + d)

According to the question,

★ Sum of the terms is -3

⇒ (a - d) + a + (a + d) = -3

⇒ a - d + a + a + d = -3

⇒ 3a = -3

⇒ a = -3 ÷ 3

∴ a = -1

Now,

★ The product of the terms is 8

⇒ (a - d) a (a + d) = 8

⇒ [(-1 - d) (-1)] (-1 + d) = 8

⇒ (d + 1)(d - 1) = 8

⇒ d² - 1 = 8 {(a + b)(a - b) = a² - b²}

⇒ d² = 8 + 1

⇒ d² = 9

⇒ d = √9

∴ d = ± 3

Case 1: If d = +3

Terms → (a - d), a, (a + d)

Numbers → (-1 - 3), -1, (-1 + 3)

∴ Numbers: -4, -1, 2

Case 2: If d = -3,

Terms → (a - d), a, (a + d)

Numbers → (-1 + 3), -1, (-1 - 3)

∴ Numbers: 2, -1, -4