Learn Implementing Series in Python

In Python, you can efficiently generate, manipulate, and visualize arithmetic and geometric series using lists and Matplotlib. These tools make it easy to model numerical patterns and analyze their behavior.

Defining an Arithmetic Series

An arithmetic series follows the formula:

def arithmetic_series(n, a, d):
    return [a + i * d for i in range(n)]

Where:

a is the first term;
d is the common difference;
n is the number of terms;
A list comprehension generates n terms of the sequence;
Each term increases by d from the previous term.

Example Calculation:


              1234
            
def arithmetic_series(n, a, d):
    return [a + i * d for i in range(n)]

print(arithmetic_series(5, 2, 3))  # Output: [2, 5, 8, 11, 14]

Defining a Geometric Series

A geometric series follows the formula:

def geometric_series(n, a, r):
    return [a * r**i for i in range(n)]

Where:

a is the first term;
r is the common ratio (each term is multiplied by r from the previous term);
n is the number of terms.

Example Calculation:


              1234
            
def geometric_series(n, a, r):
    return [a * r**i for i in range(n)]

print(geometric_series(5, 2, 2))  # Output: [2, 4, 8, 16, 32]

Plotting the Series in Python

To visualize the sequences, we plot them using matplotlib.


              1234567891011121314151617181920212223242526272829303132333435363738394041424344454647
            
import numpy as np
import matplotlib.pyplot as plt

# Define parameters
n = 10  
a = 2   
d = 3   
r = 2   

# Series generating functions
def arithmetic_series(n, a, d):
    return [a + i * d for i in range(n)]

def geometric_series(n, a, r):
    return [a * r**i for i in range(n)]

# Generate series
arith_seq = arithmetic_series(n, a, d)
geo_seq = geometric_series(n, a, r)

# Generate indices for x-axis
x_values = np.arange(1, n + 1)

# Create figure
plt.figure(figsize=(10, 5))

# Plot Arithmetic Series
plt.subplot(1, 2, 1)
plt.plot(x_values, arith_seq, 'bo-', label='Arithmetic Series')
plt.xlabel("n (Term Number)")
plt.ylabel("Value")
plt.title("Arithmetic Series: a + (n-1)d")
plt.grid(True)
plt.legend()

# Plot Geometric Series
plt.subplot(1, 2, 2)
plt.plot(x_values, geo_seq, 'ro-', label='Geometric Series')
plt.xlabel("n (Term Number)")
plt.ylabel("Value")
plt.title("Geometric Series: a * r^n")
plt.grid(True)
plt.legend()

# Show plots
plt.tight_layout()
plt.show()

How do you define an arithmetic series function in Python?

Select the correct answer

def arithmetic_series(n, a, d): 
    return [a + i * d for i in range(n)]

def arithmetic_series(n, a, d): 
    return [a * d**i for i in range(n)]

def arithmetic_series(n, a, d): 
    return [a - d**i for i in range(n)]

def arithmetic_series(n, a, d): 
    return [a * i + d for i in range(n)]

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Section 2. Chapter 5

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Defining an Arithmetic Series

An arithmetic series follows the formula:

def arithmetic_series(n, a, d):
    return [a + i * d for i in range(n)]

Where:

a is the first term;
d is the common difference;
n is the number of terms;
A list comprehension generates n terms of the sequence;
Each term increases by d from the previous term.

Example Calculation:


              1234
            
def arithmetic_series(n, a, d):
    return [a + i * d for i in range(n)]

print(arithmetic_series(5, 2, 3))  # Output: [2, 5, 8, 11, 14]

Defining a Geometric Series

A geometric series follows the formula:

def geometric_series(n, a, r):
    return [a * r**i for i in range(n)]

Where:

a is the first term;
r is the common ratio (each term is multiplied by r from the previous term);
n is the number of terms.

Example Calculation:


              1234
            
def geometric_series(n, a, r):
    return [a * r**i for i in range(n)]

print(geometric_series(5, 2, 2))  # Output: [2, 4, 8, 16, 32]

Plotting the Series in Python

To visualize the sequences, we plot them using matplotlib.


              1234567891011121314151617181920212223242526272829303132333435363738394041424344454647
            
import numpy as np
import matplotlib.pyplot as plt

# Define parameters
n = 10  
a = 2   
d = 3   
r = 2   

# Series generating functions
def arithmetic_series(n, a, d):
    return [a + i * d for i in range(n)]

def geometric_series(n, a, r):
    return [a * r**i for i in range(n)]

# Generate series
arith_seq = arithmetic_series(n, a, d)
geo_seq = geometric_series(n, a, r)

# Generate indices for x-axis
x_values = np.arange(1, n + 1)

# Create figure
plt.figure(figsize=(10, 5))

# Plot Arithmetic Series
plt.subplot(1, 2, 1)
plt.plot(x_values, arith_seq, 'bo-', label='Arithmetic Series')
plt.xlabel("n (Term Number)")
plt.ylabel("Value")
plt.title("Arithmetic Series: a + (n-1)d")
plt.grid(True)
plt.legend()

# Plot Geometric Series
plt.subplot(1, 2, 2)
plt.plot(x_values, geo_seq, 'ro-', label='Geometric Series')
plt.xlabel("n (Term Number)")
plt.ylabel("Value")
plt.title("Geometric Series: a * r^n")
plt.grid(True)
plt.legend()

# Show plots
plt.tight_layout()
plt.show()

How do you define an arithmetic series function in Python?

Select the correct answer

def arithmetic_series(n, a, d): 
    return [a + i * d for i in range(n)]

def arithmetic_series(n, a, d): 
    return [a * d**i for i in range(n)]

def arithmetic_series(n, a, d): 
    return [a - d**i for i in range(n)]

def arithmetic_series(n, a, d): 
    return [a * i + d for i in range(n)]

Everything was clear?

Thanks for your feedback!

Section 2. Chapter 5