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Question
The sum of three consecutive terms terms of an is 21 and the sum of the squares of these terms is 165. find these terms.
The sum of three consecutive terms terms of an is 21 and the sum of the squares of these terms is 165. find these terms.
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Solution
Let three consecutive terms be a-d, a, a+d
where d is common difference
a-d+a+a+d=21
3a=21
a=7
(a-d)²+a²+(a+d)²=165
a²-2ad+d²+a²+a²+2ad+d²=165
3a²+2d²=165
147+2d²=165
2d²=18
d²=9
d=3
a-d=4
a+d=10
the terms are 4,7,10
Let three consecutive terms be a-d, a, a+d
where d is common difference
a-d+a+a+d=21
3a=21
a=7
(a-d)²+a²+(a+d)²=165
a²-2ad+d²+a²+a²+2ad+d²=165
3a²+2d²=165
147+2d²=165
2d²=18
d²=9
d=3
a-d=4
a+d=10
the terms are 4,7,10
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