Python Program to Display the First 10 Terms of the Series 2, 5, 10, 17, ...

Understanding and generating series in Python can be a great way to enhance your programming skills, especially when working on sequence-based algorithms. In this article, we will explore a specific series and provide a step-by-step guide on how to write a Python program to display the first 10 terms of the series 2, 5, 10, 17, 26, 37, 50, 65, 82, and 101. We will also delve into the mathematical concept behind the series and discuss the code in detail, providing insights on how and why each line works.

Introduction to the Series

The given series 2, 5, 10, 17, 26, 37, 50, 65, 82, 101, is a special one where each term is the square of its index plus 1. This can be represented as:

For n 0, 1, 2, 3, ... the series is defined as:

an n2 1

Understanding the Code

The Python program to generate the first 10 terms of the series is as follows:

# Define the number of terms
n_terms  10
# Initialize the first term
first_term  2
# Print the first term
print(first_term, end' ')
# Initialize the difference
diff  3
# Generate and print subsequent terms
for i in range(1, n_terms):
    print(term   diff, end' ')
    term  term   diff
    diff  diff   2

Line-by-Line Explanation

n_terms 10 first_term 2 print(first_term, end' '): Prints the first term of the series, which is 2, and sets the `end` parameter to ' ' to ensure that the next number is printed on the same line without a newline. diff 3 for i in range(1, n_terms):: Iterates from 1 to 9 (since `n_terms` is 10, the range is 1 to 9). The loop will execute 9 times, generating 9 additional terms. print(term diff, end' '): The term at the current index is calculated as the previous term plus the current difference. The `end` parameter ensures the number is printed on the same line. The print statement continues until all 10 terms are printed. term term diff: Updates the current term by adding the current difference to it. diff diff 2: Increments the difference by 2 for each iteration, which is necessary to generate the correct terms in the series.

Output and Explanation

The output of the Python program is:

2 5 10 17 26 37 50 65 82 101

This output matches the series starting from the second term, as the first term is manually specified. The program correctly calculates the remaining 9 terms using the given pattern and prints them in sequence.

Further Exploration

This program can be extended or modified in several ways. For example, you can:

Add a function to calculate a given term of the series directly, given its index. Create a class to encapsulate the series and its properties. Optimize the program to handle a larger number of terms with better performance.

Understanding series and their generation can be a valuable skill, not just for coding, but also for mathematical problem-solving. Practicing with different series, such as Fibonacci, geometric, or others, can further enhance your programming and analytical skills.

Conclusion

In conclusion, the given Python program effectively demonstrates how to generate the first 10 terms of the series 2, 5, 10, 17, 26, 37, 50, 65, 82, 101. By mastering the basics of series generation, you can tackle a wide range of programming and mathematical challenges. Delving into the code, understanding its structure, and exploring further applications can significantly boost your programming prowess.