**Geometric Progression:**

A geometric series is a sequence of elements in which the next item is obtained by multiplying the previous item by the common ratio.

A G.P. Series is a number series in which the common ratio of any consecutive integers (items) is always the same.

**Formulas:**

The sum of GP ( Sn ) = a(r^n)/(1-r) Nth term (Tn) = a* r^(n-1)

where a = first term

r = common ratio

n= number of terms

Given a, r, n values, and the task is to calculate the geometric progression series.

## Program for Geometric Progression in Python

### Method #1: Using Mathematical Formula (Static Input)

**1)Printing the first n terms of Geometric Progression:**

**Approach:**

- Give the first term (a) as static input and store it in a variable.
- Give a common ratio (r) as static input and store it in another variable.
- Give the number of terms(n) as static input and store it in another variable.
- loop from 1 to gvn_n+1 using the for loop(excludes last no).
- Inside the for loop, calculate the nth term of GP using the above-given mathematical formula and store it in a variable.
- Print the above result.
- Print the nth term of GP.
- The Exit of the Program.

**Below is the implementation:**

# Give the first term (a) as static input and store it in a variable. gvn_a = 2 # Give the common ratio (r) as static input and store it in another variable. gvn_r = 3 # Give the number of terms(n) as static input and store it in another variable. gvn_n = 7 # loop from 1 to gvn_n+1 using the for loop(excludes last no) for itr in range(1, gvn_n+1): # Inside the for loop, calculate the nth term of GP using the above given # mathematical formula and store it in a variable. nth_term = gvn_a * gvn_r**(itr-1) # Print the above result print(nth_term) # Print the nth term of GP print("The nth_term of GP = ", nth_term)

**Output:**

2 6 18 54 162 486 1458 The nth_term of GP = 1458

- Python Program to Find Sum of Geometric Progression Series
- Java Program to Find Sum of Geometric Progression
- Python Program to Find the Sum of the Series: 1 + 1/2 + 1/3 + ….. + 1/N

**2)Calculating the sum of GP**

**Approach:**

- Give the first term (a) as static input and store it in a variable.
- Give a common ratio (r) as static input and store it in another variable.
- Give the number of terms(n) as static input and store it in another variable.
- Check if the given common ratio(gvn_r) value is greater than 1 using the for loop.
- If it is true, then calculate the sum of n terms of Gp using the above-given respective mathematical formula and store it in a variable.
- Else calculate the sum of n terms of Gp using the above-given respective mathematical formula and store it in a variable.
- Print the Sum of Geometric Progression(GP) of given n terms.
- The Exit of the Program.

**Below is the implementation:**

# Give the first term (a) as static input and store it in a variable. gvn_a = 2 # Give the common ratio (r) as static input and store it in another variable. gvn_r = 3 # Give the number of terms(n) as static input and store it in another variable. gvn_n = 7 # Check if the given common ratio(gvn_r) value is greater than 1 using the for loop if(gvn_r > 1): # If it is true, then calculate the sum of n terms of Gp using the above given # respective mathematical formula and store it in a variable. Sum_Gp = (gvn_a*(gvn_r**gvn_n))/(gvn_r-1) else: # Else calculate the sum of n terms of Gp using the above given # respective mathematical formula and store it in a variable. Sum_Gp = (gvn_a*(gvn_r**gvn_n))/(1-gvn_r) # Print the Sum of Geometric Progression(GP) of given n terms. print("The Sum of Geometric Progression(GP) = ", Sum_Gp)

**Output:**

The Sum of Geometric Progression(GP) = 2187.0

### Method #2: Using Mathematical Formula (User Input)

**1)Printing the first n terms of Geometric Progression:**

**Approach:**

- Give the first term (a) as user input using the int(input()) function and store it in a variable.
- Give a common ratio (r) as user input using the int(input()) function and store it in another variable.
- Give the number of terms(n) as user input using the int(input()) function and store it in another variable.
- loop from 1 to gvn_n+1 using the for loop(excludes last no).
- Inside the for loop, calculate the nth term of GP using the above-given mathematical formula and store it in a variable.
- Print the above result.
- Print the nth term of GP.
- The Exit of the Program.

**Below is the implementation:**

# Give the first term (a) as user input using the int(input()) function and store it in a variable. gvn_a = int(input("Enter some random number = ")) # Give the common ratio (r) as user input using the int(input()) function # and store it in another variable. gvn_r = int(input("Enter some random number = ")) # Give the number of terms(n) as user input using the int(input()) function and # store it in another variable. gvn_n = int(input("Enter some random number = ")) # loop from 1 to gvn_n+1 using the for loop(excludes last no) for itr in range(1, gvn_n+1): # Inside the for loop, calculate the nth term of GP using the above given # mathematical formula and store it in a variable. nth_term = gvn_a * gvn_r**(itr-1) # Print the above result print(nth_term) # Print the nth term of GP print("The nth_term of GP = ", nth_term)

**Output:**

Enter some random number = 1 Enter some random number = 2 Enter some random number = 6 1 2 4 8 16 32 The nth_term of GP = 32

**2)Calculating the sum of GP**

**Approach:**

- Give the first term (a) as user input using the int(input()) function and store it in a variable.
- Give a common ratio (r) as user input using the int(input()) function and store it in another variable.
- Give the number of terms(n) as user input using the int(input()) function and store it in another variable.
- Check if the given common ratio(gvn_r) value is greater than 1 using the for loop.
- If it is true, then calculate the sum of n terms of Gp using the above-given respective mathematical formula and store it in a variable.
- Else calculate the sum of n terms of Gp using the above-given respective mathematical formula and store it in a variable.
- Print the Sum of Geometric Progression(GP) of given n terms.
- The Exit of the Program.

**Below is the implementation:**

# Give the first term (a) as user input using the int(input()) function and store it in a variable. gvn_a = int(input("Enter some random number = ")) # Give the common ratio (r) as user input using the int(input()) function # and store it in another variable. gvn_r = int(input("Enter some random number = ")) # Give the number of terms(n) as user input using the int(input()) function and # store it in another variable. gvn_n = int(input("Enter some random number = ")) # Check if the given common ratio(gvn_r) value is greater than 1 using the for loop if(gvn_r > 1): # If it is true, then calculate the sum of n terms of Gp using the above given # respective mathematical formula and store it in a variable. Sum_Gp = (gvn_a*(gvn_r**gvn_n))/(gvn_r-1) else: # Else calculate the sum of n terms of Gp using the above given # respective mathematical formula and store it in a variable. Sum_Gp = (gvn_a*(gvn_r**gvn_n))/(1-gvn_r) # Print the Sum of Geometric Progression(GP) of given n terms. print("The Sum of Geometric Progression(GP) = ", Sum_Gp)

**Output:**

Enter some random number = 1 Enter some random number = 2 Enter some random number = 6 The Sum of Geometric Progression(GP) = 64.0