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Core 1 sigma notation help please!

The question is: Find the least value for n for which
n
Σ (4r-3) > 2000
r=1

Please show full working out and clear explanations, thanks

Reply 1

Super199

Original post by Efemena15

Please show full working out and clear explanations, thanks

! Umm do you understand what you are looking for? Start with 1 to find the first term. Sub that in to get a. Sub a few more numbers in and see if a common difference appears. Then use the formula :colone:

Reply 2

Efemena15

Original post by Super199

I've done that, but i get to the equation 2n^2-n-2000>0

I don't know what to do now, the answer in the book is 32 but i don't know how to get to that

Reply 3

m4ths/maths247

Original post by Efemena15

I've done that, but i get to the equation 2n^2-n-2000>0

I don't know what to do now, the answer in the book is 32 but i don't know how to get to that

Yes...solve the equation and n > 31. something (for the positive solution). by a quick inspection which means n will have to be the next integer

Reply 4

Efemena15

Original post by m4ths/maths247

Yes...solve the equation and n > 31. something (for the positive solution). by a quick inspection which means n will have to be the next integer

I can't factorise that! Which two numbers multiply to give 4000 but add to give -n?

(edited 10 years ago)

Reply 5

m4ths/maths247

Original post by Efemena15

I can't factorise that! Which two numbers multiply to give 4000 but add to give -n?

Why do you want to factorise it?
Is it because it's in the Core 1 book?

Reply 6

Efemena15

Original post by m4ths/maths247

Why do you want to factorise it?
Is it because it's in the Core 1 book?

Yes, so I can just leave it as 2n^2-n-2000?

Also, sir, I'm struggling with a few questions on page 99 of the C1 book, I'm assuming you have it because I've seen in a few of your videos that you've referred to questions from the book.

If you ever have the time, I need help on questions 8b, 8c and 10b please. Thanks a lot

Reply 7

alexmufc1995

Original post by Efemena15

Yes, so I can just leave it as 2n^2-n-2000?

I believe you can factorise this (roughly) by completing the square to give the required answer?

Reply 8

chocolatemonkey7

yep..i completed the square for the question, and using a calculator (i'm not sure if you're allowed to use a calculator in c1), and it gave the right answer, so try completing the square. note that n is a positive number.