# Write a c program to find out the sum of given A.P.

Levels of difficulty: / perform operation:

### Definition of arithmetic progression (A.P.):

A series of numbers in which difference of any two consecutive numbers is always a same number that is constant. This constant is called as common difference.

### Example of A.P. series:

5 10 15 20 25 …
Here common difference is 5 since difference of any two consecutive numbers for example 20 – 15 or 25 -20 is 5.

### Sum of A.P. series:

`Sn = n/2(2a + (n-1) d)`

### Tn term of A.P. series:

`Tn = a + (n-1) d `

### C Program

```#include<stdio.h>
#include<math.h>
int main() {
int a,d,n,i,tn;
int sum=0;
printf("Enter the first number of the A.P. series: ");
scanf("%d",&a);
printf("Enter the total numbers in the A.P. series: ");
scanf("%d",&n);
printf("Enter the common difference of A.P. series: ");
scanf("%d",&d);
sum = ( n * ( 2 * a + ( n -1 ) * d ) )/ 2;
tn = a + (n-1) * d;
printf("Sum of the series A.P.: ");
for (i=a;i<=tn; i= i + d ) {
if (i != tn)
printf("%d + ",i); else
printf("%d = %d ",i,sum);
}
return 0;
}
```

### Output:

```Enter the first number of the A.P. series: 1
Enter the total numbers in the A.P. series: 5
Enter the common difference of A.P. series: 3
Sum of the series: 1 + 4 + 7 + 10 + 13 = 35
```