Go to navigation
It is currently Mon Dec 05, 2016 8:38 pm

All times are UTC




Post new topic Reply to topic  [ 7 posts ] 
Author Message
PostPosted: Wed Jan 07, 2015 10:40 pm 
Offline

Joined: Fri Sep 19, 2014 4:32 pm
Posts: 189
please help is there any trick to working out this question??


Top
 Profile  
 
PostPosted: Wed Jan 07, 2015 10:52 pm 
Offline

Joined: Fri Sep 19, 2014 4:32 pm
Posts: 189
Here's the question -

We write s(2,5) as an abbreviation for 2+3+4+5 so that s(2,5) = 14

Similarly

S(6,39) = 6+7+8+9+....+ 38 + 39 = 765

Work out:

s(1,3) =
s(6,40) =
s(7, 38) =

s(1,2) - s(2,3) + S (3,4) - s(4,5)+ ......... - S (18,19) + S (19,20) =


Top
 Profile  
 
PostPosted: Wed Jan 07, 2015 11:00 pm 
Offline

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11940
We've had this before - try searching.


Top
 Profile  
 
PostPosted: Thu Jan 08, 2015 12:07 am 
Offline

Joined: Sun Sep 22, 2013 6:25 pm
Posts: 144
Location: Cheltenham
The long way round is this:

Total = (number of items) x (mean value)

For s(a,b):
number of items = b-a+1
mean value = (a+b)/2
This gives total = (b-a+1)(a+b)/2

So
s(1,3) = 1+2+3 = 6
Check the formula works: s(1,3)=(3-1+1)*(4/2)=3*2=6

Then
s(6,40)=(40-6+1)*(46/2)=35*23=805
s(7,38)=(38-7+1)*(45/2)=32*22.5=720
or alternatively s(7,38)=s(6,40)-6-39-40=805-85=720

The short way is to use the example they have given of s(6,39)=765, like this:
s(1,3)=1+2+3=6
s(6,40)=s(6,39)+40=765+40=805
s(7,38)=s(6,39)-6-39=765-45=720


Top
 Profile  
 
PostPosted: Thu Jan 08, 2015 6:38 am 
Offline

Joined: Mon Mar 03, 2014 12:10 pm
Posts: 28
This is one of those "can you spot the short way" type questions. DebsB has wonderfully given the short way to do the second and third questions, using the answer they have already given for s(6,39).

And in the final question, they're looking to see if you spot that most of the terms cancel each other out:

s(1,2) - s(2,3) + s(3,4) - s(4,5)+ ......... - s(18,19) + s(19,20)
= 1 + 2 - 2 - 3 + 3 + 4 - 4 - 5 + ... - 18 - 19 + 19 + 20
= 1 + 20
= 21


Top
 Profile  
 
PostPosted: Thu Jan 08, 2015 10:48 am 
Offline

Joined: Sun Sep 22, 2013 6:25 pm
Posts: 144
Location: Cheltenham
rah_b92 wrote:
This is one of those "can you spot the short way" type questions. DebsB has wonderfully given the short way to do the second and third questions, using the answer they have already given for s(6,39).

And in the final question, they're looking to see if you spot that most of the terms cancel each other out:

s(1,2) - s(2,3) + s(3,4) - s(4,5)+ ......... - s(18,19) + s(19,20)
= 1 + 2 - 2 - 3 + 3 + 4 - 4 - 5 + ... - 18 - 19 + 19 + 20
= 1 + 20
= 21


Nicely done, rah_b92. I hadn't even noticed that the final question was there. :oops: Shocking example of failure to read the question properly - let's hope none of our kids have been throwing marks away by missing stuff out in that way!


Top
 Profile  
 
PostPosted: Thu Jan 08, 2015 11:53 am 
Offline

Joined: Fri Sep 19, 2014 4:32 pm
Posts: 189
thank you everyone


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 7 posts ] 

All times are UTC


Who is online

Users browsing this forum: Bing [Bot] and 7 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
CALL 020 8204 5060
   
Privacy Policy | Refund Policy | Disclaimer | Copyright © 2004 – 2016