Find four numbers in AP whose sum is 20 and sum of whose square is 120.

Dear Student

Let a-3d,a-d,a+d,a+3d be 4 noumbers in Ap

According to given condition

(a-3d)+(a-d)+(a+d)+(a+3d) =20

so 4a =20 or a =5

Again

(a-3d)²+(a-d)²+(a+d)²+(a+3d)²=120

2(a²+9d²)+2(a²+d²) =120

2a²+10d²=60 or a²+5d²=30

Using a = 5 we get

5d²=5 or d = +1 or -1

So AP is 2,4,6,8 or 8,6,4,2

Regrads

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