C program to print 1 3 6 10 15 21 28 36 triangular series

C Program to Print 1 3 6 10 15 21 28 36 Triangular Series

Understanding Triangular Numbers

• Triangular numbers are a sequence of numbers where each number is the sum of all natural numbers up to that point.
• They form a triangular pattern when represented visually, as shown below:

        1
      1   2
    1   2   3
  1   2   3   4
1   2   3   4   5

• The first few triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, and so on.

Methods for Printing Triangular Numbers

There are two common methods to print triangular numbers in C:

1. Using a single loop
2. Using the formula for triangular numbers

1. Using a single loop

C

#include <stdio.h>

int main() {
    int n = 8;  // Number of triangular numbers to print
    int i, j, sum = 0;

    printf("Triangular Series:\n");

    for (i = 1; i <= n; i++) {
        sum += i;  // Calculate the current triangular number
        printf("%d ", sum);
    }

    printf("\n");

    return 0;
}

Explanation:

• The for loop iterates from 1 to n.
• Inside the loop, sum is calculated by adding the current value of i to the previous value of sum.
• The calculated sum is then printed, representing the current triangular number.

2. Using the formula for triangular numbers

C

#include <stdio.h>

int main() {
    int n = 8;
    int i;

    printf("Triangular Series:\n");

    for (i = 1; i <= n; i++) {
        int triangular = i * (i + 1) / 2;  // Formula for triangular numbers
        printf("%d ", triangular);
    }

    printf("\n");

    return 0;
}

Explanation:

• The formula i * (i + 1) / 2 directly calculates the i-th triangular number.
• The loop iterates through the desired number of terms and prints the calculated triangular numbers.

Key Points:

• Both methods produce the same output, so choose the one that you find more intuitive or efficient.
• Ensure proper indentation for readability.
• Consider using meaningful variable names to enhance code clarity.
• Validate user input to prevent unexpected behavior or errors.
• Explore different formatting options for output (e.g., vertical display, custom separators).
• Experiment with generating different triangular series (e.g., even-numbered triangular numbers, odd-numbered triangular numbers).