Fibonacci Numbers and Other Sequences

See: www.geeksforgeeks.org/program-for-nth-fibonacci-number/

Introduction

The Fibonacci numbers are integers in the following sequence

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .

In mathematical terms, the Fibonacci numbers are defined by the relationship

Fn = Fn-1 + Fn-2

with seed values F0 = 0 and F1 = 1

Project #1

Write a program that calculates Fibonacci numbers. Run the program and display the numbers (max number 100).

Display the number of the Fibonacci numbers generated.

Project #2

Write a program that calculates numbers defined by the relationship

(Xn)2 = (Xn-1)2 + (Xn-2)2

Run the program and display the numbers (max number 500).

with seed values X0 = 0 and X1 = 1.

Display the number of the Fibonacci numbers generated.

Project #3

Write a program that

Project #4

Write a program that calculates the reverse Fibonacci numbers. Run the program and display the numbers (max number + or - 100).

Fn-2 = Fn - Fn-1

with seed values F0 = 0 and F1 = 1

Note: the same sequences of numbers is generated but but with alternating signs.

Project #5

Write a program that calculates Lucas numbers. Run the program and display the numbers (max number 100).

Ln = Ln-1 + Ln-2

with seed values L0 = 2 and L1 = 1

Project #6

Write a program that calculates the reverse Lucas numbers. Run the program and display the numbers (max number + or - 100).