 # Python Program to Print nth Iteration of Lucas Sequence

In the previous article, we have discussed Python Program to Find Sum of Geometric Progression Series

Definition of Lucas sequence:

We’ve all heard of the Fibonacci sequence. It is a sequence in which each term is the sum of the two preceding terms. The Lucas sequence is the same as the previous one, but with different starting values. A Fibonacci sequence starts with 0 and 1, whereas a Lucas sequence starts with 2 and 1. The other terms in the Lucas sequence are 3, 4, 7, 11, and so on.

Given a number ‘n’ and the task is to print the given nth iteration of Lucas Sequence.

Examples:

Example1:

Input:

n = 6

Output:

The above Given nth iteration of Lucas Sequence =  18

Example 2:

Input:

n = 10

Output:

The above Given nth iteration of Lucas Sequence =  123

## Program to Print nth Iteration of Lucas Sequence

Below are the ways to get the given nth Iteration of the Lucas Sequence.

### Method #1: Using For Loop  (Static Input)

Approach:

• Give the First term =2 (since the first term in Lucas Sequence is 2 which is a constant) as static input and store it in a variable.
• Give the Second term =1 (since the second term in Lucas Sequence is 1 which is a constant) as static input and store it in another variable.
• Give the number as static input and store it in another variable.
• Loop from ‘1’ to the above given n+1 value (since doesn’t include the last term) range using For loop.
• Inside the loop, get the third term which is the sum of the first and the second term, and store it in a variable.
• Assign the value of the second term to the first term.
• Assign the value of the third term to the second term and come out of For Loop.
• Print the Value of the above given nth iteration of Lucas Sequence(i.e. first term).
• The Exit of the program.

Below is the implementation:

# Give the First term =2 (since the first term in Lucas Sequence is 2 which is a constant)
# as static input and store it in a variable.
fst_trm = 2
# Give the Second term =1 (since the second term in Lucas Sequence is 1 which is a constant)
# as static input and store it in another variable.
secnd_trm = 1
# Give the number as static input and store it in another variable.
gvn_n_vlue = 6
# Loop from '1' to the above given n+1 value (since doesn't include last term) range
# using For loop.
for i in range(1, gvn_n_vlue+1):
# Inside the loop , get the third term which is the sum of first and the second term
# and store it in a variable.
third_trm = fst_trm+secnd_trm
# Assign the value of second term to the first term.
fst_trm = secnd_trm
# Assign the value of the third term to the second term and come out of For Loop.
secnd_trm = third_trm
# Print the Value of above given nth iteration of Lucas Sequence(i.e. first term).
print("The above Given nth iteration of Lucas Sequence = ", fst_trm)


Output:

The above Given nth iteration of Lucas Sequence =  18

### Method #2: Using For Loop  (User Input)

Approach:

• Give the First term =2 (since the first term in Lucas Sequence is 2 which is a constant) as static input and store it in a variable.
• Give the Second term =1 (since the second term in Lucas Sequence is 1 which is a constant) as static input and store it in another variable.
• Give the number as User input and store it in another variable.
• Loop from ‘1’ to the above given n+1 value (since doesn’t include the last term) range using For loop.
• Inside the loop, get the third term which is the sum of the first and the second term, and store it in a variable.
• Assign the value of the second term to the first term.
• Assign the value of the third term to the second term and come out of For Loop.
• Print the Value of the above given nth iteration of Lucas Sequence(i.e. first term).
• The Exit of the program.

Below is the implementation:

# Give the First term =2 (since the first term in Lucas Sequence is 2 which is a constant)
# as static input and store it in a variable.
fst_trm = 2
# Give the Second term =1 (since the second term in Lucas Sequence is 1 which is a constant)
# as static input and store it in another variable.
secnd_trm = 1
# Give the number as User input and store it in another variable.
gvn_n_vlue = int(input("Enter Some Random number = "))
# Loop from '1' to the above given n+1 value (since doesn't include last term) range
# using For loop.
for i in range(1, gvn_n_vlue+1):
# Inside the loop , get the third term which is the sum of first and the second term
# and store it in a variable.
third_trm = fst_trm+secnd_trm
# Assign the value of second term to the first term.
fst_trm = secnd_trm
# Assign the value of the third term to the second term and come out of For Loop.
secnd_trm = third_trm
# Print the Value of above given nth iteration of Lucas Sequence(i.e. first term).
print("The above Given nth iteration of Lucas Sequence = ", fst_trm)


Output:

Enter Some Random number = 10
The above Given nth iteration of Lucas Sequence = 123

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