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c1 maths question annoying me

Okay I can do part a and part b 1 but not part b2 - its driving me mad and I can't understand why the markscheme has got what its got on it
This is the question
8. (a) Prove that the sum of the first n positive integers is given by
1/2 n(n + 1). (4)
(b) Hence, find the sum of
(i) the integers from 100 to 200 inclusive,
(ii) the integers between 300 to 600 inclusive which are divisible by 3. (5)

Answer to b 1 is 15150

on the mark scheme for part b 2
All they have given is 15150 X 3
why why ?
and how else could you get the answer - its driving me mad - just as I thought I was fine :C
It says hence - so don't you have to use the formula n/2(n+1)
b)i)One way of doing it is the (Sum of the first 200 natural numbers) - (Sum of the first 99 natural numbers).
b)ii) It can be written as 3(100+101+102....200). See why they've given it as 15150 x 3?
Reply 2
Avatar for snafle
snafle
Think about the numbers you have-

[100->200] 100, 101, 102, 103 etc
[300->600] 300, 303, 306, 309 etc

sneaky edit there Glutamic :wink:
Reply 3
Avatar for Doji
Doji
17
100 - 200 both inclusive, means 101 numbers in there...

a=100,l=200[br][br]101[100+200]÷2[br][br]=101(300)÷2a= 100, l=200[br][br]101[100 + 200] \div 2[br][br]= 101(300) \div 2
Reply 4
Avatar for Doji
Doji
17
2nd one...

300 - 600 (both are divisible by 3)

so, a = 300, l = 600

But how many terms are divisible by 3 between the range they gave?

300 ..303...306 ... (d=3)

300 + (n-1)3 = 600 <== We equate it to 600, as its the largest possible value in the range that is divisible by 3, and it will give the highest n value, i.e. the highest term that is divisible by 3, and thus the number of terms.

Now we rearrange:

3n - 3 = 600 - 300

3n - 3 = 300

3n = 303

n = 101 (101 terms are divisible by 3)

101[300 + 600]/2

= 45450
Doji, you're right, but the question says 'hence', implying it wants to you to use the formula for the sum of the first n natural numbers. Sometimes it says 'hence, or otherwise' though. I'm not entirely sure how it's marked, you may lose method marks for doing that.
Reply 6
Avatar for Doji
Doji
17
Yeah i realised, she did say how else she could get it though ... you would probably lose 1 or 2 marks... although its solomon after all, i doubt edexcel will ask stuff like this, but can't be under prepared!
Reply 7
Avatar for snafle
snafle
Surely it's bad practice to give the answer away immediately, instead just give a hint? You learn far more that way.
Reply 8
Avatar for Doji
Doji
17
snafle
Surely it's bad practice to give the answer away immediately, instead just give a hint? You learn far more that way.


well i stuggled over this question so thought ym explanation could help her, i checked the asnwer out, and the method helped me, not the answer :smile:
Reply 9
Avatar for HiyaLulu
HiyaLulu
could you please post a link to the markcheme?
Reply 10
Avatar for Notnek
Notnek
21
Original post by HiyaLulu
could you please post a link to the markcheme?

This is a 9 year old thread.

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