## INDEX

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

C Code:

#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;
}

Sample 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

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: