Question

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

Answer 1

Let the numbers are 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

d² = 4

d = +2

Hence, the numbers are 5, 7 and 9 when d = 2 and 9, 7 and 5 when d = -2. In both the cases numbers are the same.