The document discusses patterns and sequences found in several example problems. It then explains how to use a TI-83 calculator to find the nth term of a sequence. Specifically, it shows that the sequence 4, 7, 10, etc. increases by 3 each term. It also explains how to set up the calculator by changing the mode to sequence, setting the minimum value to 1, defining the function U(n) = U(n-1) + 3, and setting the initial value U(1) = 4 to find any term such as the 100th term.

1. SequenceS

2. Here we did some problems on patterns and sequences.. 4, 7, 10.. 3, 6, 12.. 32, 16, 8..

3. Here are the answers to the problems. 4, 7, 10,.. 13, 16, 19 3, 6, 12,.. 24, 48, 96 32, 16, 8,.. 4, 2, 1 1, 1, 2, 3, 5, 8, 13,.. 24, 34, 55 How did we get the answer??

4. 0 1 2 3 4 5 6 7 N These numbers that are listed 1 through 7 is called “Rank”. N is the number of the list. We use N to shortcut through the common difference. By using the 1 st problem ( 4, 7, 12,…) 1 4 7 1013 16 19 22 3 3 3 3 3 3 3 If we look carefully we can see that the pattern goes by 3’s. How did we find out? We found 3 as the “Common difference” by subtracting the 2 nd number to the 1 st . *But what if we wanted to find the 100 th number?*

5. What if we wanted to find the 100th number? 1 4 7 1013 16 19 22 1 2 3 4 5 6 7 N 0 3 3 3 3 3 3 3 100? First of all we need to use the TI-83 to do this. We want to go to “MODE” and change “Func.” to “Seq.” (for sequence) Now we go to the “Y=“ screen. So we put nMin = 1 U(n) = u(n-1)+3 because we’re going to add 3 every time. U(nMin) = 4 Because we are starting at the number 4

6. Now you exit to your main screen. Then you hit “u(100) to find the 100 th number To be continued.. Sorry..