1800-150-456-789
FlagBACK
Flag Algebra> progresions...
question mark

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?

santosh p , 13 Years ago
Grade 12
anser 2 Answers
Pavan Kumar

Last Activity: 13 Years ago

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}

Kushagra Madhukar

Last Activity: 4 Years ago

Dear student,
Please find the solution to your problem.
 
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 = Σ(a + (n – 1)d)2
= Σ(c/2 + (n – 1)c)2
= c2 Σ(n2 – n + 1/4)
= c2n(4n2 – 1)/12
 
Thanks and regards,
Kushagra

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Other Related Questions on algebra

question mark
What is a binomial expression?
algebra
1 Answer Available

Last Activity: 1 Year ago

question mark
Can we divide two vectors? If this is possible then how?
algebra
1 Answer Available

Last Activity: 1 Year ago

question mark
How do you write “the product of 18 and q” as an algebraic expression?
algebra
1 Answer Available

Last Activity: 1 Year ago

question mark
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
algebra
0 Answer Available

Last Activity: 2 Years ago

question mark
Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?
algebra
1 Answer Available

Last Activity: 2 Years ago