1. RECURSION & CALCULATOR Calculators are magic!! We can get the calculator to determine each term in a sequence. We input the sequence just like the recursion formula. For the first sequence: 2, 4, 6, 8, … u 1 = 2u n = u n-1 + 2 Input the first term: {2}Hit enter Input the change formula:{ans(1)+2} Hit enter Keep hitting enter for each subsequent term.

2. FINDING THE nth TERM We have to count the terms ourselves. We can have the calculator count for us. We need to tell it that the 1 st term is 2. {1, 2}Hit enter Then tell it to count the first term and add 2 to the 2 nd term. {Ans(1)+1,Ans(2)+2}Hit enter The calculator will give us the term first and the value second.{2, 4}, {3, 6} What is the 17 th term?

3. u 0 = 427u n = u n-1 – 17 Find the 18 th term. {0, 427}Hit enter {ans(1)+1, ans(2)-17} {18, 121}

4. RECURSION FORMULAS The calculators we have allow us to put the recursion formula directly into the calculator and build a table or a graph. First, we have to put the calculator into sequence mode. Normally, we are in function mode. Hit MODE and select SEQ Now, go to y= This is where we can put in the formula

5. nMin = 1 –This is asking what the first value of n is: If you know u 0, nMin = 0. If you know u 1, nMin = 1. It will default to 1. u(n) = –This is where we put in the formula. Since the calculator cannot do subscripts, it puts the subscript in parenthesis: u n = u(n) u n-1 = u(n – 1) u(nMin) = –You will put in the first term here. Remember what you put in for nMin.

6. Tables and Graphs Once you have the recursion formula in y =, you can set up the window to view your graph. The WINDOW sets the ranges of x-axis and y- axis that is displayed on your screen. TABLESET does for the table what WINDOW does for the graph. It sets where the table starts and the increments for the x values (in this case the n values) TABLE shows you the values in a table

7. GEOMETRIC SEQUENCES We can do the same with a geometric sequence. u 1 = 2u n = 1.8u n-1 Find the 21 st term. {1, 2}Hit enter {ans(1)+1, ans(2)*1.8} {21, 254964.7} Magic!!