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. Refer to the For Loop in C programming.

#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 C Program is the same as above. However, we separated the logic using C 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;
}

C Program to find Sum of Arithmetic Progression Series

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