SOLUTION: Pleas help me answer this problem : In an arithmetic progression.The sum of the first three terms is 18,and the sum of the squares of these terms is 126,Find the terms.

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Question 703202: Pleas help me answer this problem : In an arithmetic progression.The sum of the first three terms is 18,and the sum of the squares of these terms is 126,Find the terms.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
d = common difference
x = second term (I think that may make it easier)
first term = x-d
third term = x%2Bd
The sum of the first three terms is
%28x-d%29%2Bx%2B%28x%2Bd%29=18 --> 3x=18 --> highlight%28x=6%29
The sum of the squares of these terms is
%286-d%29%5E2%2B6%5E2%2B%286%2Bd%29%5E2=126
6%5E2-12d%2Bd%5E2%2B6%5E2%2B6%5E2%2B12d%2Bd%5E2=126
6%5E2%2B6%5E2%2B6%5E2%2B2d%5E2=126
3%2A6%5E2%2B2d%5E2=126
3%2A36%2B2d%5E2=126
3%2A36%2B2d%5E2=126
108%2B2d%5E2=126 --> 2d%5E2=126-108 --> 2d%5E2=18 --> d%5E2=18%2F2 --> d%5E2=9
There are two solutions:
either d=3 or d=-3
Either way, the terms are
6-3=highlight%283%29, highlight%286%29 and 6%2B3=highlight%289%29