Animation introduction

Can you draw the following picture on your calculator?

arrow in first position

No? Try this. List the coordinate points in clockwise order. Make sure to end where you began.

These coordinates can be stored in a list. Use \( L_1 \) for x-coordinates and \( L_2 \) for y-coordinates. For example, \( \{ 1, 2, 3 \} \rightarrow L_1 \).

After your lists are stored, use the STATPLOT command to select options.

GRAPH to see if your lists are correct.

Now, can you make the arrow move without finding all the new coordinates?

arrow in second position

No? What do you think will happen with something like \( L_1 +10 \rightarrow L_1 \)? Try it to find out.

Loop introduction

Recall that the Fibonacci sequence can be defined by: \( F_1 = 1, F_2 = 1, F_n = F_{n-1} + F_{n-2} \text{ for } n \ge 3 \).

Please type the following commands to find the 25th Fibonacci number.

        : 1→A
        : 1→B
        : FOR(I,3,25,1)
        : A+B→C
        : B→A
        : C→B
        : END
        : Disp "25TH FIBONACCI NUM: "
        : Disp C

Run the program. Be prepared to discuss the following questions:

  1. What does the FOR command do?
  2. What does the first number of FOR do?
  3. What does the second number of FOR do?
  4. How can you change this program to find the "Nth" Fibonacci? (assume \(N \ge 3\))