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


ans:n(4n2-1)c2/3


 


HOW?

2 years ago

Share

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)


 


=c^{2}\left(\frac{n(n+1)(2n+1)}{6}-\frac{n(n+1)}{2}+\frac{n}{4}\right)


 


=\frac{c^{2}n(4n^{2}-1)}{12}

2 years ago

Post Your Answer

More Questions On Algebra

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
A certain polynomial P(x),x E R WHEN DIVIDED BY (x-a),(x-b) and (x-c) leaves remainder a,b,c.then find the remainder when P(x) is divided by (x-a)(x-b)(x-c) where a,b,c are distinct
 
 
it is clear that f(a) is the remainder when f(x) is divided by x-a and when f(x) is divided by q(x) the remainder will be having degree less than q(x) so when P(x) is divided by...
  img
MuraliKrishna Medavaram 5 months ago
 
Thanks and Regards, M.MURALIKRISHNA askIITians faculty
  img
MuraliKrishna Medavaram 5 months ago
 
The polynomial P(x) - x has roots a,b, and c Hence P(x) - x = (x-a)(x-b)(x-c) Q(x) for some polynomial Q(x) or P(x) = Q(x) (x-a)(x-b)(x-c) + x It immediately follows that the remainder when...
 
mycroft holmes 5 months ago
(2x+3y) is divisible by 17,then for what value of k; (9x+ky) is divisible by 17. Please give the solution.
 
 
gcd(2x+ 3y, 9x + ky ) = 17 or gcd(2x + 3y, (9x + ky) - 4(2x + 3y)) = 17 or gcd(2x + 3y, (x + (k-12) y) = 17 gcd ( 2x+ 3y - 2(x + k- 12y), (x + (k-12) y)) = 17 so 27y -2k y is divisible by 17...
  img
Sher Mohammad 2 months ago
 
Please reply fast
 
Shrey 3 months ago
 
4(2x+3y)+(9x+5y) = 17(x+y). Since RHS is divisible by 17, and so is 4(2x+3y), we must have 9x+5y also divisible. Hence for any k such that k = 5+19m for any integer m, we have 9x+ky...
 
mycroft holmes 3 months ago
Is the function f (x) = |x^2 - x| differentiable at x = 2. If yes find it’s derivative.
 
 
Yes fuction will be differentiable at x =2. which can easily be seen by graph of the function. First draw the graph of y = x2-x and then take mode. Derivative will be = 2x-1 at x= 2...
  img
ruchi yadav 4 months ago
 
Yes, for x>1, the f(x) = x^2 - x It if a polynomial function. Hence it is differentiable at x=2. Thanks & Regards Bharat Bajaj askIITians Faculty
  img
bharat bajaj 4 months ago
 
yes, for x>1 f(x)=x^2-x f'(x)=2x-1 f'(2)=4-1 Sher Mohammad B.Tech, IIT Delhi
  img
Sher Mohammad 4 months ago
Two forces of 60N and 80N acting at an angle of 60degrees with eath other. Pull an object. What single pull will replace the given forces. What is the direction of the force. The answer is...
 
 
Dear student, The resultant force would be given by: The direction would be given by: Now, lets place the 60 N force along the horizontal direction so the 80 N force would be making an angle...
  img
Sumit Majumdar 18 days ago
 
Hi, your answer is correct and the book one’s too. The difference between the answers is their representation. You are saying 34.7 degrees with the 80 N force and the book says 25.28...
  img
bharat bajaj 18 days ago
If a^x=b b^y=c c^z=a Prove xyz=1 Please give the solution
 
 
a x =b => x=log a b b y =c=> y=log b c c z =a=> z=log c a xyz=(log a b.log b c).log c a =log a c.log c a =log a a =1 Thanks & Regards Rinkoo Gupta AskIITians Faculty
  img
Rinkoo Gupta one month ago
 
a^xyz =(a^x)^yz =b^yz =(b^y)^z =c^z =a by comparision xyz=1 proved Sher Mohammad faculty askiitians
  img
Sher Mohammad one month ago
 
a^x=b b^y=c =>a^xy=c c^z=a =>a^xyz=a =>xyz=1
 
pramod Gopinath one month ago
Rationalise denominator 1/2+√3.
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 18 days ago
View all Questions »