C1 Value Of N Watch

footballhead
Badges: 4
Rep:
?
#1
Report Thread starter 12 years ago
#1
HI SAY IF YOU WANT TO FIND THE SUM OF THE NATURAL NUMBERS upto 100
from 1

is n = 100 or 101,

also for example say some of all the even numbers etc upto 100, is it 50?


and sorry one more, say they give you last term as 20 and first term as 10, are the n values 10 or is 11?!


AHHHHHH
0
reply
ProfessorFitBoy
Badges: 2
Rep:
?
#2
Report 12 years ago
#2
For your first query:

Sn = n (a+l)/2

Sn = 100 (1+100) / 2

Sn = 5050
0
reply
Trevor 12345
Badges: 0
Rep:
?
#3
Report 12 years ago
#3
(Original post by footballhead)
HI SAY IF YOU WANT TO FIND THE SUM OF THE NATURAL NUMBERS upto 100
from 1

is n = 100 or 101,

also for example say some of all the even numbers etc upto 100, is it 50?


and sorry one more, say they give you last term as 20 and first term as 10, are the n values 10 or is 11?!


AHHHHHH


Count it on your Fingers or Toes.......???

10 11 12 13 14 15 16 17 18 19 20.......11 terms of course

from ath to bth term is always b-a+1 terms
0
reply
TheDuck
Badges: 2
Rep:
?
#4
Report 12 years ago
#4
If you write all the numbers out...say 1 to n, you get

1,2,3......,n

and then in reverse order

n,n-1,......3,2,1

Then add both these up you get (n+1)+(n+1)..... n times
So n*(n+1) gives twice the sum of the numbers from 1 to 100.
So to get the sum you divide my two...i.e. n(n+1)/2 as mentioned.

If you want to find the sum of the numbers from 50 to 100 say. Then you can calculate the sum of the numbers from 1 to 100 and then subtract the sum of the numbers from 1 to 49.

For the even numbers, you could write them out as before
2,4,6.....2(n-1),2n
2n,2(n-1),....6,4,2

But then you can see that we have exactly the same numbers before but just times two...i.e. the total sum here will be twice that of the sum of the numbers from 1 to n
i.e. n(n+1). However, dont forget that n is the number of numbers you are adding up, so for n=10, in the first example you had 1+2+3...+9+10 but in the second it is 2+4+6....+20. So if you want the sum of the even numbers from 1 to 20, you have to divide n by 2 to get the value for n..i.e. the highest number in your sum is actually 2n. So the formula is actually n/2(n/2+1)=n^2/4+n/2 where n is the biggest (and presumably even) number in the sequence.

E.g. Say n(biggest number)=6, then sum=6^2/4+6/2=9+3=12=2+4+6 as needed.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • Cardiff Metropolitan University
    Undergraduate Open Day - Llandaff Campus Undergraduate
    Sat, 27 Apr '19
  • University of East Anglia
    Could you inspire the next generation? Find out more about becoming a Primary teacher with UEA… Postgraduate
    Sat, 27 Apr '19
  • Anglia Ruskin University
    Health, Education, Medicine and Social Care; Arts, Humanities and Social Sciences; Business and Law; Science and Engineering Undergraduate
    Sat, 27 Apr '19

Have you registered to vote?

Yes! (551)
37.84%
No - but I will (114)
7.83%
No - I don't want to (102)
7.01%
No - I can't vote (<18, not in UK, etc) (689)
47.32%

Watched Threads

View All
Latest
My Feed