Question

Find three numbers in an A.P. whose sum is 12, and product is 60.

Answer 1

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

The sum of the three numbers is 12

(a − d) + a + (a + d) = 12

3a = 12

⇒ a = 4

So the numbers are 4 − d, 4, 4 + d

The product of the three numbers is 60

(4 − d) × 4 × (4 + d) = 60

4(16 − d²) = 60

64 − 4d² = 60

4d² = 4

⇒ d² = 1

⇒ d = 1

Final numbers = 4 − 1, 4, 4 + 1

= 3, 4, 5

The three numbers in A.P. are 3, 4, and 5.