Question

Find four numbers in A.P. whose sum is 32 and sum of squares is 276.​

Answer 1

Answer:

Let us take the four numbers in A.P. to be a−3d,a−d,a+d,a+3d.

Thus, their sum = 4a=32

⇒a=8.

The sum of their squares is 2(a

2

+d

2

)+2(a

2

+9d

2

)=4a

2

+20d

2

=276

⇒a

2

+5d

2

=69

⇒5d

2

=69−64=5, implying d to be 1.

The numbers are thus 5,7,9,11