How to Write a C Program to Generate the Sequence 1 4 10 19 31 46 67 91 118 141... Up to 10000?

The sequence provided is generated based on a specific pattern. By examining the differences between consecutive terms, we can observe that the differences themselves form a sequence that increases by 1 for each term. This pattern is crucial for understanding and generating the sequence in a C program.

Understanding the Pattern and Differences

The given sequence is: 1, 4, 10, 19, 31, 46, 67, 91, 118, 141, ...

The differences between terms are: 3, 6, 9, 12, 15, ... This can be described by the formula for the nth term of the difference sequence: 3n, where n starts from 1.

Generating the Sequence in C

To generate the sequence in C and continue until we reach or exceed 10000, we can use the following code:

#include stdio.hint main() {    int term  1;  // The first term of the sequence    int n  1;     // Counter for the term number    int limit  10000;  // The upper limit for the sequence    while (term  limit) {        // Calculate the next term        term  3 * n   term - 3;        // Print the current term        printf("%d ", term);        // Increment the counter        n  ;    }    return 0;}

Explanation of the Code

Initialization:

term 1: The first term of the sequence is set to 1.

n 1: The counter for the term number is initialized to 1.

limit 10000: The upper limit for the sequence is set to 10000.

Loop:

while (term limit): The loop continues as long as term is less than limit.

term 3 * n term - 3: The next term is calculated by adding 3*n to the current term. The -3 adjustment ensures that we skip the 6th multiple of 3.

printf("%d ", term): The current term is printed.

n : The counter n is incremented for the next iteration.

Note: This code will print the sequence up to the first term that is greater than or equal to 10000.

Alternative Approach: Manual Input

Alternatively, you can create a C program that manually takes the number of terms to generate. Here is an example:

int main() {    int inf;    printf("Enter number of Terms: ");    scanf("%d", inf);    printf("Series: ");    for (int i  0; i  inf; i  ) {        int f  1;        for (int j  0; j  i; j  ) {            f  f   3;        }        printf(" %d ", f);    }    return 0;}

Explanation of the Alternative Code

Initialization:

inf: The number of terms to generate is input by the user.

printf("Enter number of Terms: ");: A prompt is displayed for the user to enter the number of terms.

scanf("%d", inf);: The user's input is stored in the inf variable.

printf("Series: ");: A message is displayed to indicate the start of the series.

Loop:

for (int i 0; i inf; i ): The outer loop runs for the specified number of terms.

f 1: The initial term is set to 1.

for (int j 0; j i; j ): The inner loop calculates the difference between terms (3n) and adds it to the current term.

printf(" %d ", f): The current term is printed.

Note: The series output will stop after the specified number of terms or until inf iterations.

Pattern Observations

By examining the differences between terms, we can see that the differences form a sequence that increases by 3 and skips every sixth term:

1 and 4: Difference is 3 (3x1)

4 and 10: Difference is 6 (3x2)

10 and 19: Difference is 9 (3x3)

19 and 31: Difference is 12 (3x4)

31 and 46: Difference is 15 (3x5)

46 and 67: Difference is 21 (3x7, skips the 6th multiple)

When running the loop until 10000, the difference will follow the pattern of 3n, skipping the 6th multiple.

Example Output

Here is an example of the output for 10 terms:

Series: 1 4 10 19 31 46 67 91 118 141

As you can see, the differences between terms follow the pattern of multiples of 3, with the 6th multiple skipped.

Thank you for reading this article. If you have any questions or further insights, feel free to reach out!