Question

The sum of four numbers in AP is 20 and the sum of their squares is 120 find the numbers

Answer 1

Let the first number = a + 3d

Second number = a + d

Third Number = a - d

Fourth number = a - 3d

a+ 3d + a + d + a - d + a - 3d = 20

4a = 20

a = 5

Now,

(a+3d)² + (a+d)²+(a-d)² + (a-3d)² = 120

a² + 9d² + a² + d² + a² + d² + a² + 9d² = 120

4a² + 20d² = 120

a² + 5d² = 30

(5)² + 5d² = 30

5d² = 5

d² = 1

d = √1

d = 1

Now,

A.P.

= a + 3d , a +d , a-d , a-3d

= 5 +3 , 5 + 1 , 5 - 1 , 5 - 3

= 8,6,4,2......