Fibonacci and Golden Ratio: Problem Solving

Question 1

Determine the 60th term in the Fibonacci sequence using Binet’s Formula.
a. 1.258626903x10^10
b. 1.548008756x10^12
c. 956722026041

Answer 1

b. 1.548008756x10^12

Question 2

Consider the Fibonacci Sequence. F(n)= 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
Compute: (F14)^3 - 6 (F25)
a. 277,229
b.535,432,483
c.546,562,495

Answer 2

b.535,432,483

Question 3

compute the mean of the first 9 numbers of the Fibonacci series.
a. 9.9
b. 10.8
c. 9.8

Answer 3

c. 9.8

Question 4

if the width of a rectangular lot is equal to 138.67m, then what must be the length in order for it to be a golden rectangle?
a.224.37
b.174.34
c. 222.26

Answer 4

a.224.37

Question 4

if the length of a rectangular lot is equal to 235m what must the width be in order for it to be a golden rectangle?
a.120.65
b. 134.50
c. 145.33

Answer 4

c. 145.33

Question 5

One side of a golden rectangle is 25 m. which of the following is a measure for the other side?
a. 14. 20
b. 15.45
c. 12. 36

Answer 5

b. 15.45

Question 6

Find the Fibonacci number when n = 9, using the recursive formula.
a. 54
b. 21
c. 13

Answer 6

b. 21

Question 7

Find the next three terms of the sequence 15, 23, 38, 61, …
a. 99, 160, 559
b. 98, 157, 550
c. 89, 200, 260

Answer 7

a. 99, 160, 559

Question 8

The 17th term in the sequence is 1597. Find the next term.
a. 2985
b. 2368
c. 2584

Answer 8

c. 2584