### 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