# 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.

## C Arithmetic Progression Series

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.

In Mathematical 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``````

## C Program to return 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;
}```