Homework Help

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

user profile pic

tonyah995 | Student, Undergraduate | Salutatorian

Posted October 2, 2010 at 1:11 PM via web

dislike 1 like

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

2 Answers | Add Yours

user profile pic

william1941 | College Teacher | Valedictorian

Posted October 2, 2010 at 1:24 PM (Answer #1)

dislike 2 like

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.

user profile pic

neela | High School Teacher | Valedictorian

Posted October 2, 2010 at 1:25 PM (Answer #2)

dislike 1 like

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.

 

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes