T-Totals coursework - finding the nth term?

Could you give more details over the coursework. I'm not familiar with the title, but might be able to help if you say more what it's about.

Right, thanks.

(Never hear of this course work before...sounds interesting).

So you start by labelling a general t-shape with the values of each number in terms of n.

The bottom on is n, like you say.

The one above that is n-9

The the top of the t-shape has entries n-17, n-18 and n-19.

Add these up an you get the total for the sum of the numbers in any general t-shape on the 9x9 grid as being 5n-63

Hope that helps.

Yeah that does help, but are there any other techniques to finding this nth term?

What do you mean?

That is the best, easiest way.

In your coursework you'd be expected to find some totals for different positioned t-shapes, then have a go a generalising the out come, maybe predicting the total for another few t-shapes. You could generate a sequence starting with n=20, then n=21, n=22, n=23 up to the highest n you can fit on in that row and find the nth term of that sequence using the usual method of looking at differences.

Fromthere you coul check your predictions and try generalise the result to show the nth term is true for any t-shape by doing what I did above.

To get decent marks you'd then need to extend the work to differnet problems. Do at least one of these: look at differnet shapes, different sized t-shapes, different sized grids. You'd need to exactly the same for at least one of these changes. It may even be possible to try and fin a general formula for the each problem using two-variable instead of just n (eg for the total sum of numbers in a t-shape with t-number n in an m by m grid).

For really top marks youd have to introduce some math which is not part of your GCSE course...this is where Ii'm stuck right now on how to advise you. I can't think what you could do right now.

That all sounds good make sure you mention the 9x9 grid is a numbere from b to b+80 an not a 9x9 grid lifted off a larger grid....if you don't understand me here don't worry....just leave it.

Can I ask what grade you are aiming for, as this will tell me how far you need to take the course work/whether you need the last part with 'new' maths or not.

I'm predicted an A but I'd like to aim for A*. I get confused with coursework, I can do it fine when I'm in the school enviroment but when I take it home to redraft my mind just goes blank.
In my notes I have the following calculations:

5 x 20 – 63 = 37
5 x 21 – 63 = 42
5 x 22 – 63 = 47
5 x 29 – 63 = 82
5 x 38 – 63 = 127
5 x 47 – 63 = 172

The calculations are used to express the nth term but I'm unsure as to what I should be writing about them- I surely can't just insert the calculations. Could you explain a bit more about the b to b+80 grid please?
Thanks

Your calculations are using your forumla to work out the total of certain t-shapes.

You can check your claculation against adding up the actual numbers in those t-shapes.

As for the b to b+80 grid...

...well you started off with the grid with numbers 1 to 81 (1 = b, 81 = b+80)

You could start with any 9x9 grid with 81 consecutive numbers (eg if the first number was 50, your b to b+8 would be 50 to 130.

This is opposed to taking a 9x9 grid from a larger number grid for example, ig you were to pick a 4x4 gri from a 10 x 10 grid you could have the following to draw your grid on

3 4 5 6
13 14 15 16
23 24 25 25
33 34 35 36

Which would get you very different answer

i have the generic formula 5n-7x, x being the grid size e.g.
5x20=100 7x9=63
100-63=37
where does 7 come from?

i know they change each time by 7, but why 7, there must be some reason it's 7 each time