Question

The sum of the three numbers in AP is 21 and the product of the first and third numbers of the sequence is 45. What are the three numbers?

Options

• 5, 7 and 9

• 9, 7 and 2

• 3, 7 and 11

• 4 and 3

Answer 1

5, 7 and 9

Explanation:
Let the numbers be a - d, a, a + d
Then, a - d + a + a + d = 21
⇒ 3a = 21
⇒ a = 7
and (a - d)(a + d) = 45
⇒ a² - d² = 45
⇒ 49 - d² = 45
⇒ d² = 4 ⇒  d = ±2
Hence, the numbers are 5, 7 and 9 when d = 2
and 9, 7 and 5 when d = -2