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
Let a,b,c E R and a (is not equal to 0) be such that (a+c) 2 2, then the quadratic equation ax 2 + bx + c = 0 has : Imaginary roots. Real roots. Exactly one real root lying in the...
 
 
Hello student, Please find my response to your question below Iam unable to interpret your query Because you didot mention the condition clearly here so without condition you may not get an...
  img
SHAIK AASIF AHAMED 5 months ago
 
Hello student, Please find my response to your question below What does the line’a (is not equal to 0) be such that (a+c) 2 ’mean it does not have a meaning i think there should...
  img
SHAIK AASIF AHAMED 5 months ago
 
in the first line it is (a+c)^2
 
Ujjwal 5 months ago
x 1/2 +y=11,x+y 1/2=7
 
 
Hello student, Please find the answer to your question below From(1): x^(1/2) = 7 - y , Letx (1/2) +y=11...........(1) x+y (1/2) =7..........(2) Squaring both sides: x = (7-y)^2 = y^2 - 14y...
  img
SHAIK AASIF AHAMED 4 months ago
If the equation z 3 +(3+i)z 2 -3z- (m+i)=0, where m is a real number, has at least one real root, then m can have the value equal to Answer: 1 or 5
 
 
Let a,b,c be the roots. If a is real, (b,c are conjugates) a+b+c=3+i abc=m+i ab+bc+ca=-3 Use this information and solve for m....
  img
Ravi 2 months ago
 
Solution:
 
mycroft holmes 2 months ago
Please answer 14 and 15 question of the image below
 
 
please upload a different image , the questions in the image are not clear, i can’t help you untill you post the questions clearly, please post the questions clearly.
  img
Sher Mohammad 6 months ago
 
Hello student, Please find answer to your question 14. 15.
  img
Jitender Singh 6 months ago
If the vertices of triangles are placed at (1.8,2.4),(5,0) and (0,0), then where is the orthocentre located? The answer is given as (1.8,2.4) Please explain
 
 
Solution: As we know the.. orthocentre is the point of intersection of altitudes of the triangle... soo for right angle triangle.. orthocenter is the vertex itself on which right angle is...
  img
Ajay Verma 6 months ago
If anything divided by 0 is “not defined”, then can we say that 0 multiplied by any number which is “not defined’ is 1. So that the number which cannot be defined does have a value which...
 
 
No, we cannot apply any mathematical/logical operations on these nos as they by there name are not defined. So any mathematical operation is invalid....
  img
Yash Baheti 4 months ago
View all Questions »