1800 2000 838

CART 0

• 0

MY CART (5)

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping

X

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

                                        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

More Questions On Algebra

Post Question

Vouchers
To Win!!!
[(5-2root 6) power (x 2 -1) ]+ [(5 + 2 root 6) power (x 2 -1) =

HInt. Use the log operator solve it. Thanks.

 Vijay Mukti 25 days ago
2 PLUS 2

 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.

 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%

I think 10%

 Hasan Naqvi 2 months ago

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...

 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 »