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
If set of values of “a” for which f(x) =ax^2 -(3+2a)x+6, a is not equal to zero is positive for exactly three distinct negative integral values of x is (c,d) then the value of (c^2+16 d^2)...
 
 
Hello student, Please find the answer to your question below Givenf(x) =ax^2 -(3+2a)x+6 =(ax-3)(x-2) Here roots of equation f(x)=0 are 2 and 3/a and f(0)=6 f(x) should be positive for...
  img
SHAIK AASIF AHAMED 2 months ago
Find all real values of m for which the inequalty mx 2 - 4x + 3m + 1 >0 is satisfied for all positive x. Hint : THE GIVEN EXPRESSION IS +VE ONLY AND ONLY FOR POSTIVE x.
 
 
Hello Student, Please find the solution The value of this quadratic is always positive (>0) So graph will always be above x-axis therefore the condition will be :- D>0 and a>0...
  img
Nishant Vora one month ago
1)If all the roots (zeros) of the polynomial f(x)=x^5+ax^4+bx^3+cx^2+dx-420 are integers larger than 1, then f(4)=? 2)Consider the two functions f(x) =x^2+2bx+1 and g(x)=2a(x+b), where the...
 
 
Hello student, Please find the answer to your question below f must have 5 (not necessarily distinct) roots d1, d2, . . . d5. f factors as (x – d1)(x – d2)(x – d3)(x...
  img
SHAIK AASIF AHAMED 2 months ago
PLZ HELP STUCK WITH THIS FOR HOURS!! A regular hexagon ABCDEF with centre O,show that: __ __ __ __ 1.OB - OA = OC - OD __ __ __ __ 2.OD + OA = 2OB + OF __ __ __ __ 3.AD + EB + FC = 4AB
 
 
Something missing in the question. Concepts that are useful here length of points from center all equal. Triangle formed by center and 2 consecutive points is equilateral. Arun Kumar IIT...
  img
Arun Kumar 5 months ago
A straight line makes an intercept on the y-axis twice as long as that on the x-axis and is at a unit distance from the origin. Determine its equation.
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 3 months ago
Differential of log^n x
 
 
Ans: Thanks & Regards Jitender Singh IIT Delhi askIITians Faculty
  img
Jitender Singh 3 months ago
View all Questions »