Question

The sum of first three terms of an ap is 15 if the sum of their squares is 93 find the AP

Answer 1

Let the first three terms are (a-d), a, (a+d).

Now sum of 1st three terms is 15

→ (a-d) + a + (a+d) = 15

→ 3a = 15

→ a = 5

Sum of their Square is 93

→ (a-d)² + a² + (a+d)² = 93

→ a² + d² - 2ad + a² + a² + d² + 2ad = 93

→ 3a² + 2d² = 93

Put a = 5

so, 3(5)² + 2d² = 93

→ 2d² = 93 - 75 = 18

→ d² = 9

→ d = 3, -3

So there are two AP's with the given conditions: (a-d), a, (a+d)

1st AP: when d=3

AP is : 2, 5, 8

2nd AP: when d = -3

AP is : 8, 5, 3