Question

Find three numbers in A.P. whose sum is 9 and the sum of their squares is 35.

Answer 1

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

The sum of the three numbers is 9

(a − d) + a + (a + d) = 9

3a = 9

⇒ a = 3

So the numbers are 3 − d, 3, 3 + d

(3 − d)² + 3² + (3 + d)² = 35

(9 − 6d + d²) + 9 + (9 + 6d + d²) = 35

27 + 2d² = 35

2d² = 8

⇒ d² = 4

⇒ d = 2

3 − 2, 3, 3 + 2

1, 3, 5

The three numbers in A.P. are 1, 3, and 5.