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find the three numbers in an arithmetic progression whose sum is 48 and the sum of their squares is 800
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One can present the three consecutive terms of the AP as
x -d, x, x + d,
where x is the mid term and d is the common difference.
Then the sum of the tree terms is 3x, and you can easily find a from the equation
3x = 48,
which implies x = = 16.
Now the sum of squares of the tree terms is
= = = .
It gives you an equation to find d:
= ---> = = 32 ---> = = 16.
Hence, d = +/- 4.
It gives the AP terms as 12, 16 20, or 20, 16, 12.
Answer. AP terms are 12, 16 20, or 20, 16, 12.