• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Number pattern

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!!!!!!!
 
32,573
4,303
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.
 
2,434
85
Start by tabulating values of N and N squared.
 
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!!!!!
 
32,573
4,303
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.
 

Related Threads for: Number pattern

  • Posted
2 3
Replies
58
Views
19K
  • Posted
Replies
8
Views
3K
  • Posted
Replies
0
Views
2K
  • Posted
Replies
5
Views
2K
  • Posted
Replies
1
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top