If the sum of first n terms of an A.P. is cn2, then sum of squares of these n terms is?




2 years ago


Answers : (1)


If a is 1st term and d is common difference, sum of n terms = (n/2) (2a + (n-1)d) = (2an-nd) + n2d


comparing this with cn2 we get : 2an-nd = 0  and  d = c    =>    a = c/2,  d = c


sum of squares of n terms = \sum_{r=1}^{n}(a+(n-1)d)^{2}


=\sum_{r=1}^{n}\left( \frac{c}{2}+(n-1)c\right)^{2}


=\sum_{r=1}^{n}c^{2}\left( n^{2}-n+\frac{1}{4}\right)


=c^{2}\left( \sum_{r=1}^{n}n^{2}-\sum_{r=1}^{n}n+\sum_{r=1}^{n}\frac{1}{4}\right)





2 years ago

Post Your Answer

More Questions On Algebra

Ask Experts

Have any Question? Ask Experts
Post Question
Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details
A man wanted to get into his work building, but he had forgotten his code. However, he did remember five clues. These are what those clues were: The fifth number plus the third number equals...
3 possibilities from 1,2,3,4 but as the sum is 30 answer will b 74658
purva 4 months ago
Code is 74658
Asha 4 months ago
tushar 4 months ago
Solve this Question: There are four people in a house. A fireman, an athlete, an old woman and a drunk guy. The house catches fire and before the fact is known, it is too late. All they know...
first fireman and athlete will go- 2 minutes then fireman will return- 1 minute then old lady and drunk man will go- 5 minutes then athlete will return- 2 minutes then fireman and athlete...
Ketan Jain 4 months ago
first fireman and athlete(2) go athelete stays while fireman(3) returns. Then woman and drunk guy go(8) and athlete returns(10) Then athlete and fireman go together(12) :D Solved
Sashank Gambhira 4 months ago
--- >> fire man +ath 2 min --- >old woman +drunk guy 5 min --- > fireman +ath 2 min Total 12 min
dinesh 4 months ago
The solution set of |x +1/x| + |x +1| = (x+1)^2 /|x|
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
Arun Kumar 22 days ago
|z1|=12 |z2-3-4i|=5 |z1-z2| minimum =?
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
Arun Kumar 21 days ago
when going east at 10 kmph a train moving with const. velocity appears to be moving exactly north east . when my velocity is increased to 30 kmph east it appears to be moving north. a.what...
Hello You should apply concept of reletive velocity here Now you can find everything. Thanks & Regards Arun Kumar Btech IIT Delhi Askiitians faculty
Arun Kumar one month ago
Ok ok..is it because angle is 45 degree so...x- component and y- component must b equal????.. Am I right Sir???
shalini one month ago
Thanq very much Sir :) but why should x-10 be equal to y??? :/
shalini one month ago
View all Questions »