C Program to find Sum of Arithmetic Progression Series

Write a C Program to find the Sum of the Arithmetic Progression Series (A.P. Series) using Mathematical formulas and without using Math formulas.

Arithmetic Series is a sequence of terms in which the next element is obtained by adding a common difference to the prior item. Or A.P. series is a series of numbers in which the difference between any two consecutive numbers is always the same. It is called a common difference. The Mathematical formula behind calculating Arithmetic Progression Series:

Sum of A.P. Series : Sn = n/2(2a + (n – 1) d)
In term of A.P. Series: Tn = a + (n – 1) d

C Program to find Sum of Arithmetic Progression Series Example

This program allows the user to enter the first value, the total number of elements in a series, and the common difference. Next, it will find the sum of the Arithmetic Progression Series. Here, we used For Loop to display the A.P series, which is optional.

#include <stdio.h>

int main() {
    
    int a, n, d, tn, i;
    int sum = 0;
    
    printf(" Please Enter First Number of an A.P Series:  ");
    scanf("%d", &a);
    printf(" Please Enter the Total Numbers in this A.P Series:  ");
    scanf("%d", &n);
    printf(" Please Enter the Common Difference:  ");
    scanf("%d", &d);
    
    sum = (n * (2 * a + (n - 1) * d)) / 2;
    tn = a + (n - 1) * d;
    printf("\n The Sum of Series A.P. : ");
    for(i = a; i <= tn; i = i + d)
    {
        if(i != tn)
            printf("%d + ", i);
        else
            printf("%d = %d", i, sum);
    }
    printf("\n");
    return 0;
}

 Please Enter First Number of an A.P Series:  1
 Please Enter the Total Numbers in this A.P Series:  4
 Please Enter the Common Difference:  5

 The Sum of Series A.P. : 1 + 6 + 11 + 16 = 34

C Program to calculate the Sum of Arithmetic Progression Series using While Loop

This C Program is the same as above. However, we used While Loop to display the optional A.P Series

#include <stdio.h>

int main() {
    
    int a, n, d, tn, i;
    int sum = 0;
    
    printf(" Please Enter First Number of an A.P Series:  ");
    scanf("%d", &a);
    printf(" Please Enter the Total Numbers in this A.P Series:  ");
    scanf("%d", &n);
    printf(" Please Enter the Common Difference:  ");
    scanf("%d", &d);
    
    sum = (n * (2 * a + (n - 1) * d)) / 2;
    tn = a + (n - 1) * d;
    i = a;
    printf("\n The Sum of Series A.P. : ");
    while(i <= tn)
    {
        if(i != tn)
            printf("%d + ", i);
        else
            printf("%d = %d", i, sum);
        i = i + d;
    }
    printf("\n");
    return 0;
}

 Please Enter First Number of an A.P Series:  2
 Please Enter the Total Numbers in this A.P Series:  6
 Please Enter the Common Difference:  3

 The Sum of Series A.P. : 2 + 5 + 8 + 11 + 14 + 17 = 57

Sum of Arithmetic Progression Series without Math Formula

In this Program, we are not using any C Programming Mathematical formula.

#include <stdio.h>

int main() {
    
    int a, n, d, value, i;
    int sum = 0;
    
    printf(" Please Enter First Number of an A.P Series:  ");
    scanf("%d", &a);
    printf(" Please Enter the Total Numbers in this A.P Series:  ");
    scanf("%d", &n);
    printf(" Please Enter the Common Difference:  ");
    scanf("%d", &d);
    
    value = a;
    printf("\n A.P. Series : ");
    for(i = 0; i < n; i++)
    {
        printf("%d  + ", value);
        sum = sum + value;
        value = value + d;
    }
    printf("\n The Sum of A.P Series until %d = %d\n", n, sum);
    return 0;
}

 Please Enter First Number of an A.P Series:  2
 Please Enter the Total Numbers in this A.P Series:  6
 Please Enter the Common Difference:  7

 A.P. Series : 2  + 9  + 16  + 23  + 30  + 37  + 
 The Sum of A.P Series until 6 = 117

Sum of Arithmetic Progression Series using Functions

This Program is the same as above. However, we separated the logic using Functions.

#include <stdio.h>
int sumofAP(int a, int n, int d)
{
    int sum = (n * (2 * a + (n - 1) * d)) / 2;
    return sum;
}
int main() {
    
    int a, n, d;
    int sum = 0;
    
    printf(" Please Enter First Number of an A.P Series:  ");
    scanf("%d", &a);
    printf(" Please Enter the Total Numbers in this A.P Series:  ");
    scanf("%d", &n);
    printf(" Please Enter the Common Difference:  ");
    scanf("%d", &d);
    
    sum = sumofAP(a, n, d);

    printf("\n The Sum of Arithmetic Progression Series is =  %d\n", sum);
    return 0;
}