1. Go look at those web pages. The quiz will have a similar picture for you to draw in the spirals for. You need to draw the spirals, and tell how many there are.

2. Explain how you can get the golden ratio from the Fibonacci numbers (include some examples to make it clear what you are saying).

My answer When you divide a Fibonacci number by the number that comes right before it in the sequence*, you get a number that is close to the golden ratio. When you divide do this with big Fibonacci numbers you get a better approximation than when you use smaller numbers**. For example 13/8=1.625 is closer to the golden ratio than 3/2=1.5*** is.

To get full credit your answer must include the fact that *the Fibonacci numbers you are dividing or are making a ratio/fraction with are right next to each other in the Fibonacci sequence, **that the approximation gets better (you get closer to the golden ratio) when you use bigger Fibonacci numbers, and you must *** include some examples. You will not get full credit if you say that the ratio of Fibonacci numbers is equal to the golden ratio (each such ratio is a good approximation, but is not equal to the golden ratio).

3. For each of these sequence rules and starting numbers, tell the next 4 numbers in the sequence:

A. Rule: 2D_n + D_n+1 = D_n+2 ; Starting numbers: D₁= 3 and D₂= 1

My work: 2*3+1=7;
2*1+7=9;
2*7+9=23

My answer: 3, 1, 7, 9, 23, ...

B. Rule: E_n + 2E_n+1 = E_n+2 ; Starting numbers: E₁= 3 and E₂= 1

My work: 3+2*1=5;
1+2*5=11;
5+2*11=27

My answer: 3, 1, 5, 11, 27, ...

C. Rule: 3F_n + 2F_n+1 = F_n+2 ; Starting numbers: F₁= 3 and F₂= 2

My work: 3*3+2*2=13
3*2+2*13=32
3*13+2*32=103

My answer: 3, 2, 13, 32, 103, ...