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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