Question

Urgent Help......Pleasee

The sum of the series \( \bf 45^2-43^2+44^2-42^2+43^2-41^2+42^2-40^2.....\) to 30 terms is:-
a)2000
b)1590
c)2143
d)2220

Answer 1

When i solve it, i got 7020.

Am i right?

Answer 2

@ash2326 @Callisto @Hero

Answer 3

@ganeshie8 @kropot72 @skullpatrol

Answer 4

Help me Pleaseeeeee

Answer 5

i got 2220

Answer 6

how?

Answer 7

kinda lazy non-maths way: excel
n1 =45
n30 =29
sum of the positives = 21940
sum of the negatives = -19720
sum of these = 2220

Answer 8

Well, I think it's of the form a_n= [(46-n)^2 - (44-n)^2]
starting at n=1

Answer 9

whatever number you plug in for n, all other numbers but the first positive and last negative should cancel since this is a telescoping series.

Answer 10

help me by applying A.P formula

Answer 11

\[45^2 - 43^2 + 44^2 - 42^2 + 43^2 - 41^2 + 42^2 - 40^2+...\]=(45+43)(45-43) + (44+42)(44-42)+(43+41)(43-41)+(42+40)(42-40)+...
=2(88+86+84+82+...)

The sum there is a A.P. sum

Answer 12

I get 3540 when n = 30, but since I don't think they expect you to find that, if you plug in n = 15 (will result in 30 terms total) I get 2220 as well.

Answer 13

like this:

Answer 14

@Callisto i got 176,172,168,......

Answer 15

@hartnn can you help me?

Answer 16

then, a = 176 and d=-4
in this way, i got 3540

Answer 17

Hmm, make good use of factorization.

\(45^2−43^2+44^2−42^2+43^2−41^2+42^2−40^2+...\) <- 30 terms
Factorize every TWO terms by the formula \(a^2-b^2 = (a+b)(a+b)\)
=(45+43)(45-43) + (44+42)(44-42)+(43+41)(43-41)+(42+40)(42-40)+... <- 15 terms
= (88(2) + 86(2) + 84(2) + 82(2) + ...
Factorize again by taking out the common factor "2"
=2(88+86+84+82+...)

There are 15 terms in the sum, and the sum is a AS

Answer 18

AS = arithmetic sequence.
I suppose you know how to work out the sum for it

Answer 19

maybe you took
n=30
actually n=15 as callisto explained

Answer 20

oh! i got now.....thank you guys....

Answer 21

or you could logic it out:
45 and 44 are the only positive non-repeating numbers in the first 30 terms of the series
30 and 29 are the only negative non-repeating numbers in the first 30 terms of the series
all the rest are cancelled out
so:
45^2 + 44^2 = 3961
-(30^2)+ -(29^2) = -1741
3961-1741 = 2220

Answer 22

I literally said that. that's the definition of a telescoping series.

Answer 23

u said the first and the last numbers tho dude, it;s actually the first 2 and the last 2...