Write a program that first invites the user to input a natural number n. Then compute the nth number in the sequence (x subscript n) and display it appropriately to the user.

Question

The sequence x_n is defined, for n > 2, by the recursive formula

x_n = 2x_{n - 1} + x_{n - 2} where x₁ = 2 and x₂ = 3.

Write a program that first invites the user to input a natural number n. Then compute the n-th number in the sequence x_n and display it appropriately to the user.

(The solution has to be in the Python programming language!)

Answer 1

# Get a positive integer n from the user and return it

def getN():

while True: # Keep iterating until user gives valid input

n = int(input("Please enter n: "))

if (n >= 1):

return n # Return valid user input

print("Sorry, your input n must be at least 1.") # and make hin try again

# This method returns the n-th element of the sequence

def xN(n):

if (n == 1): # This case requires no computation

return 2 # x1 = 2 as given in specs

# Initialize for the initial case n = 2

xMinus1 = 2 # x1 = 2 the variable xMinus1 always represents x(n-1)

x = 3 # x2 = 3 the variable x will always represent x(n)

# Case n == 1 is handled as special in the if-statement

# Case n == 2 has been handled by the assignment x = 3, which is the value of x2

# Case n >= 3 is handled by the loop below

# Perform n-2 iterations of the sequence

for i in range(2, n): # i = 2, 3, 4, ..., n-1

xMinus2 = xMinus1 # x(n-2) = x(n-1) from previous iteration

xMinus1 = x # x(n-1) = x(n) from previous iteration

x = 2*xMinus1 + xMinus2 # x(n) is calculated by the given formula

return x # The latest x(n) is the final value

# Read in the user's n value and print x(n)

print(xN(getN()))