C program to print 2 15 41 80 132 197 275 366 numbers

Understanding the Number Series

• This series doesn’t follow a standard arithmetic or geometric progression.
• It has a unique pattern that involves a combination of operations.
• To generate this series in C, we’ll need to determine the mathematical formula that defines it.

Deriving the Formula for the Series

1. Observe the Differences:
   • Calculate the differences between consecutive terms:
     • 15 – 2 = 13
     • 41 – 15 = 26
     • 80 – 41 = 39
     • 132 – 80 = 52
   • Notice that the differences themselves are increasing by a constant value of 13.
2. Generalize the Formula:
   • Represent the terms as T1, T2, T3, …
   • Based on the observed pattern, the formula can be expressed as:
     • T2 = T1 + 13
     • T3 = T2 + 26 = T1 + 13 + 26
     • T4 = T3 + 39 = T1 + 13 + 26 + 39
     • And so on, with the difference increasing by 13 each time.
3. Simplify the Formula:
   • Rewrite the formula in terms of the term number (n):
     • Tn = T1 + 13(n-1) + 13(n-2) + ... + 13
   • Using the sum of arithmetic series formula, this simplifies to:
     • Tn = T1 + (13/2)(n-1)(n)

Implementation in C

C

#include <stdio.h>

int main() {
    int n = 8;  // Number of terms to print

    printf("Number Series:\n");

    for (int i = 1; i <= n; ++i) {
        int term = 2 + (13/2) * (i - 1) * i;  // Apply the formula
        printf("%d ", term);
    }

    printf("\n");

    return 0;
}

Explanation:

1. The formula 2 + (13/2) * (i - 1) * i is used to calculate each term.
2. The for loop iterates from 1 to n (8 in this case) to generate and print the terms.

Output:

Number Series:
2 15 41 80 132 197 275 366

Key Points:

• Analyzing the pattern and deriving the formula is crucial for generating such non-standard series.
• The C code effectively implements the formula to produce the desired output.
• You can modify the value of n to print a different number of terms.
• Consider adding comments within the code to explain the formula and logic for better readability.