Math 115

Quiz 9 Name: __ key __

Note: *you
may find it helpful to make a list of the first several Fibonacci numbers in
the margin*

1.
Compute the following (

a.

*This is:
the 6 ^{th} Fibonacci number + 2 =
8+2=10*

b.

*This is:
The (6+2) ^{nd} = 8^{th} Fibonacci number, or 21*

2.
Let denote the golden ratio, ,
as usual. Calculate (on your calculator, please!) and give your
answer to 5 decimal places:

3.
For the sequence that begins {10, 20, 30, 40, …}

a.
Give a recursive formula for a_{n}:

*along** with the initial condition: a _{1}=10*

b.
Given an explicit formula for a_{n}:

4.
Find the dimensions of the shaded rectangle to
make it a gnomon for the white rectangle:

6 inches *(Note: figure
not*

* drawn to scale)*

2 inches

*The larger rectangle (white and shaded combined)
must be 3 times as long as it is tall, so it is 18 inches long*

*This makes the shaded part 6 inches tall and
16 inches long.*