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 6th Fibonacci number  + 2  =       8+2=10

b.

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

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

a.       Give a recursive formula for an:

along with the initial condition:  a1=10

b.      Given an explicit formula for an:

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.