Click to Chat

1800 2000 838

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 550 off
USE CODE: EXAM25

				   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?


3 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 = $\sum_{r=1}^{n}(a+(n-1)d)^{2}$

$=\sum_{r=1}^{n}\left( \frac{c}{2}+(n-1)c\right)^{2}$

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

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

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

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

3 years ago

rank of matrix ?

The number of non-zero rows in the row reduced form of a matrix is called the row-rank of the matrix.

 Vijay Mukati 6 months ago

the no. of non zero rows in a matrix is called as rank of a matrix ….it is determined by echelon form

 kalyan 5 months ago
the minimum value of ab + bc + cd + de + ef + fg if a + b + c + d + e + f + g=1 if a,b,c,d,e,f,g >0

IT SOULD BE WHAT IS THE MAXIMUM VALUE! we know (a+b+c+d+e+f+g)^2=a^2+b^2+c^2+d^2+e^2+f^2+g^2+2(sum of numbers taken twice at a time).....................(say) here we have to find sum of...

 arvind 20 days ago

IT SOULD BE WHAT IS THE MAXIMUM VALUE! we know (a+b+c+d+e+f+g)^2=a^2+b^2+c^2+d^2+e^2+f^2+g^2+2(sum of numbers taken twice at a time).....................(say) here we have to find sum of...

 arvind 20 days ago

IT SOULD BE WHAT IS THE MAXIMUM VALUE! we know (a+b+c+d+e+f+g)^2=a^2+b^2+c^2+d^2+e^2+f^2+g^2+2(sum of numbers taken twice at a time).....................(say) here we have to find sum of...

 arvind 20 days ago
find the coefficient of x^4 in the expansion of (1+x-2x^2)^7

IN THE EXPANSION (1+X-2X 2 ) 7 THE COEFICIENT OF X 4 IS 4*7C 2 +7C 3 *6+7C 4 IN THIS EXPANSION YOU HAVE TO THINK CAREFULLY

 RAMCHANDRARAO one month ago

 jagdish singh singh one month ago

 jagdish singh singh one month ago
solve it...

The trace of a matrix is the sum of the elements of the principle diognal. for given matrix principle diognal elements are -4,-1,1.. ThereforeT r (A)=-4-1+1 =-4.

 PRAPULPODISHETTI 5 months ago

hi The trace of a matrix is the sum of the elements of the principle diognal. for given matrix principle diognal elements are -4,-1,1.. ThereforeT r (A)=-4-1+1 =-4.

 Ankit Jaiswal 9 days ago

trace matrix is equals to diognal elements so(A)=-4-1+1 =-4. r diognal elements are -4,-1,1 T

 SHANMUKESHWAR 5 months ago
How to master trigonometry problems of IIT level?

In my opinion, the best book for practicing iit level trigonometry problems is S.L. Loney (arihant publication) and Amit M. Agarwal (Arihant Publicatio

 Vaibhav Gupta 6 months ago

Right. Thanks a lot sir

 SAHIL 6 months ago

 Vaibhav Gupta 6 months ago
explain about nth root of demoivres theorm with an example?

Let z = r(cosθ + i sinθ), and let n be a positive integer. Then zn = rn(cos nθ + i sin nθ) 1 Page 2 (i.e. in taking the nth power of z, we raise the modulus to its nth power and multiply...

 SHANMUKESHWAR 4 months ago
View all Questions »

• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: R 15,000
• View Details
Get extra R 3,750 off
USE CODE: EXAM25

Get extra R 550 off
USE CODE: EXAM25

More Questions On Algebra