# Number pattern

#### orthovector

anybody know how I can relate N with t???

when N=1 t=0, N=2 t=1, N=3 t=3, N=4 t=6, N=5 t=10, N=6 t=15, N=7 t=21...and so on.

i need to derived a formula that relates N to t.

HELP!!!!!!!

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#### Mark44

Mentor
Each increment in t jumps by one more than the preceding increment. The t-sequence is {0, 1, 3, 6, 10, 15, 21, ...}

There's a way to solve this using difference equations (which are something like differential equations, but not the same). In this problem the first differences are 1, 2, 3, 4, and so on, and the second differences are all 1.

The technique escapes me at the moment, and I'm heading off to bed. In the meantime, you might try a search for "difference equations" and see if that helps you.

Start by tabulating values of N and N squared.

#### orthovector

Each increment in t jumps by one more than the preceding increment. The t-sequence is {0, 1, 3, 6, 10, 15, 21, ...}

There's a way to solve this using difference equations (which are something like differential equations, but not the same). In this problem the first differences are 1, 2, 3, 4, and so on, and the second differences are all 1.

The technique escapes me at the moment, and I'm heading off to bed. In the meantime, you might try a search for "difference equations" and see if that helps you.
thanks mark, I'll try to work on it a bit more....I think these number patterns are very interesting....

help!!!!!

#### Mark44

Mentor
This is actually a bit simpler than I first thought. Here are the numbers you gave, plus a few more, assuming they follow the same pattern
Code:
N |1|2|3|4| 5| 6| 7| 8| 9|
---------------------------
t |0|1|3|6|10|15|21|28|37|
First, I'd like to get rid of t, and switch to aN, since I would like to be able to identify which value in the second row I'm talking about. The bottom row has values of ai, where i >= 1. I stared at the table for a while, then noticed this pattern:
a1 = 0
a2 = a1 + 1
a3 = a2 + 2
a4 = a3 + 3
.
.
.
aN = ? + ?

That should get you started.

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