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

                                        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

More Questions On Algebra

Post Question

Vouchers
To Win!!!
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...

 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...

 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...

 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...

 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

 Arun Kumar 3 months ago
Differential of log^n x

Ans: Thanks & Regards Jitender Singh IIT Delhi askIITians Faculty

 Jitender Singh 3 months ago
View all Questions »