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

 

 

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 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.