Implementing Series in Python
In mathematics, series are sequences of numbers that follow a specific pattern. Two fundamental types of series are:
- Arithmetic series, where each term increases by a constant difference;
- Geometric series, where each term is multiplied by a constant ratio.
In Python, we can generate, manipulate, and visualize these series efficiently using lists and Matplotlib.
Defining an Arithmetic Series
An arithmetic series follows the formula:
Where:
ais the first termdis the common differencenis the number of terms- A list comprehension generates
nterms of the sequence. - Each term increases by
dfrom the previous term. Example Calculation:
1234def 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:
Where:
ais the first termris the common ratio (Each term is multiplied byrfrom the previous term.)nis the number of terms
1234def 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.
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647import 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()
1. How would you plot an arithmetic series in Python using matplotlib?
2. What will be the output of this code?
3. What Python function can you use to generate an arithmetic series with a first term of 2 and a common difference of 4?
4. How do you define an arithmetic series function in Python?
¿Todo estuvo claro?
¡Gracias por tus comentarios!
Sección 2. Capítulo 5
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In mathematics, series are sequences of numbers that follow a specific pattern. Two fundamental types of series are:
- Arithmetic series, where each term increases by a constant difference;
- Geometric series, where each term is multiplied by a constant ratio.
In Python, we can generate, manipulate, and visualize these series efficiently using lists and Matplotlib.
Defining an Arithmetic Series
An arithmetic series follows the formula:
Where:
ais the first termdis the common differencenis the number of terms- A list comprehension generates
nterms of the sequence. - Each term increases by
dfrom the previous term. Example Calculation:
1234def 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:
Where:
ais the first termris the common ratio (Each term is multiplied byrfrom the previous term.)nis the number of terms
1234def 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.
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647import 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()
1. How would you plot an arithmetic series in Python using matplotlib?
2. What will be the output of this code?
3. What Python function can you use to generate an arithmetic series with a first term of 2 and a common difference of 4?
4. How do you define an arithmetic series function in Python?
¿Todo estuvo claro?
¡Gracias por tus comentarios!
Sección 2. Capítulo 5
