The sum of the three numbers is equal to 15 and the sum of the squares is equal to 83

Because it's an arithmetic sequence, so
Let three numbers be A-D, a, a + D
therefore
a-d+a+a+d=15①
(a-d)²＋a²＋(a+d)²=83②
From (1) to (2)
3a=15
a=5
From (2) to (3)
3a²＋2d²=83
2d²=83-75=8
d²=4
That is, d = 2 or - 2
therefore
The three numbers are: 3,5,7
Or 7,5,3

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