anonymous
  • anonymous
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.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
So is the top line 1 1 ? And no line above that?
anonymous
  • anonymous
yeah its just 1 1.
anonymous
  • anonymous
if you can find a pattern without the 1s though, i can probably manipulate it

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nikvist
  • nikvist
\[\frac{n(n+1)}{2}-r(n-r)\quad ,\quad r=0,\dots,n\]
anonymous
  • anonymous
i know it says youre a lifesaver, but you really are a lifesaver. :) how did you find it?
anonymous
  • 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.
anonymous
  • 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.
anonymous
  • 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)
anonymous
  • anonymous
you mean the (n-r)?
anonymous
  • anonymous
Yes, that, unless you called it + r(r-n)
anonymous
  • 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.
anonymous
  • 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! :)
anonymous
  • anonymous
well your ramblings were useful. both of you were.
anonymous
  • anonymous
^_^

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