MY CART (5)

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping

X

“Hurray! You have won the gift voucher. Redeem your points now."

X

                   

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

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
[(5-2root 6) power (x 2 -1) ]+ [(5 + 2 root 6) power (x 2 -1) =
 
 
HInt. Use the log operator solve it. Thanks.
  img
Vijay Mukti 25 days ago
2 PLUS 2
 
 
answer is 2+2 = 4
 
A M S ARUN KRISHNA yesterday
 
4
 
noogler yesterday
Solve : 5(5^x+5^-x)=26
 
 
Dear Student. Assume 5 x = y and then try to solve the quadratic equation in terms of y. Then replace back the orginial value of y and find the value of x. Thanks.
  img
Vijay Mukti 4 days ago
 
5(5 x + 5 -x ) = 26 let 5 x = y so 5 - x = 1/y 5(y + 1/y) = 26 5( (y2 + 1)/y ) = 26 (y2 + 1)/y = 26/5 so 5 x = 5 x = 1
 
Abishek arun 4 days ago
what will be the value of (1%) 1/2 in terms of percentage only
 
 
IN MY OPINION ANSWER IS 10%
 
ng29 2 months ago
 
i think it would be 10%
 
grenade 2 months ago
 
I think 10%
 
Hasan Naqvi 2 months ago
please help anyone............jitendra sir where are you please help ….....
 
 
Ans: Hello Student, Please find answer to your question below sinx should be b/w 0 & 1 (with both excluded) Since base(sinx) is less than 1. So when we cancel it out, inequality sign...
  img
Jitender Singh 9 months ago
 
jitendra sir in third step .inequality sign changes why ? /............ thanks for your help ….…....
 
milind 9 months ago
Show that ln(1+x)>x for all x>0.
 
 
question printed is incorrect.Correct question:- Show that ln(1+x)0.
 
subham mohanty one month ago
View all Questions »