What is the sum of n terms of the series 1, 4, 9, 16, 25, 36 . Theyare not in AP or GP.

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william1941's profile pic

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

You are absolutely right. The series given is not an AP or a GP as neither is the difference between consecutive terms common nor is the ratio of consecutive terms the same. But if you notice carefully the series is just made up by the squares of consecutive numbers. 1= 1^2 , 4= 2^2 , 9= 3^3, 16= 4^2 , 25= 5^2 and so on.

Now the relation for the sum of the first n squares is given by the relation: n*(n+1)*(2n+1) / 6

Therefore the sum of the first n terms of the series is

= n*(n+1)*(2n+1) / 6.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To find the sum 1+4+9+16++25+36+....

This could be written in the form;

Sn = 1+2^2+3^2+....n^2 which is equal to n(n+1)(2n+1)/6.

 

 

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