Find three terms in A.P., whose sum is 15 and the sum of whose squares is 83.

Asked by Amuthavalli Thayyal Gopala Krishnan | 23rd Nov, 2013, 08:36: PM

Expert Answer:

Let the three numbers in AP be a-d, a, a+d
Then, 
sum = a-d+a+a+d=15
3a = 15
So, a = 5
 
Also, Sum of squares = 83
(a-d)2+a2+(a+d)2=83
(5-d)2+25+(5+d)2=83
25+d2-10d+25+25+d2+10d=83
75+2d2=83
2d2=8
d=+2 or -2
 
When d = 2,
The numbers are 3, 5, 7
When d = -2,
The numbers are 7, 5, 3

Answered by  | 23rd Nov, 2013, 11:43: PM

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