anonymous 5 years ago Can you help me with this patten? its a triangle like this: 1 1 3 2 3 6 4 4 6 10 7 6 7 10 15 11 9 9 11 15 and its supposed to be a triangle, like pascal's or something. I need to find a general statement for the (r+1)th element in the nth row.

1. anonymous

So is the top line 1 1 ? And no line above that?

2. anonymous

yeah its just 1 1.

3. anonymous

if you can find a pattern without the 1s though, i can probably manipulate it

4. nikvist

$\frac{n(n+1)}{2}-r(n-r)\quad ,\quad r=0,\dots,n$

5. anonymous

i know it says youre a lifesaver, but you really are a lifesaver. :) how did you find it?

6. anonymous

Are you familiar with triangular numbers? It was presumably something based on them (see first element in each row), and it was just a question of finding what that variant was. Admittedly, I didn't do it, but I grew out of these type of problems a while ago.

7. anonymous

okay thank you. i just need to know because it was like an investigation for a precalc class where we need to find it and then explain how we found it. i actually got the first part on my own but i was having a hard time with the r(n-r) part.

8. anonymous

Well the (r-n) part kind of suggests itself because the last term is always equal to the first, but after that, yeah, just guesswork (as far as I can tell)

9. anonymous

you mean the (n-r)?

10. anonymous

Yes, that, unless you called it + r(r-n)

11. anonymous

yeah. thank you so much, i was mad my teacher gave this to us and made us figure it out by ourselves. you saved my life.

12. anonymous

Haha, hardly (I didn't work it out) - but if you weren't getting me confused with the person who posted it and found my ramblings useful, then thanks! :)

13. anonymous

well your ramblings were useful. both of you were.

14. anonymous

^_^