C program to find the sum of arithmetic progression series

Problem

Find the sum of an arithmetic progression series, where the user has to enter first number, total number of elements and the common difference.

Solution

Arithmetic Progression (A.P.) is a series of numbers in which the difference of any two consecutive numbers is always the same. Here, total number of elements is mentioned as Tn.

Sum of A.P. Series: Sn = n/2(2a + (n – 1) d)
Tn term of A.P. Series: Tn = a + (n – 1) d

Algorithm

Refer an algorithm given below to find the arithmetic progression.

Step 1: Declare variables.
Step 2: Initialize sum=0
Step 3: Enter first number of series at runtime.
Step 4: Enter total number of series at runtime.
Step 5: Enter the common difference at runtime.
Step 6: Compute sum by using the formula given below.
   sum = (num * (2 * a + (num - 1) * diff)) / 2
Step 7: Compute tn by using the formula given below.
   tn = a + (num - 1) * diff
Step 8: For loop
   i = a; i <= tn; i = i + diff
   i. if(i != tn)
      printf("%d + ", i);
   ii. Else,
      printf("%d = %d", i, sum);
Step 9: Print new line

Program

Following is the C Program to find the sum of arithmetic progression series−

#include <stdio.h>
int main() {
   int a, num, diff, tn, i;
   int sum = 0;
   printf(" enter 1st no of series: ");
   scanf("%d", &a);
   printf(" enter total no's in series: ");
   scanf("%d", &num);
   printf("enter Common Difference: ");
   scanf("%d", &diff);
   sum = (num * (2 * a + (num - 1) * diff)) / 2;
   tn = a + (num - 1) * diff;
   printf("\n sum of A.P series is : ");
   for(i = a; i <= tn; i = i + diff){
      if(i != tn)
         printf("%d + ", i);
      else
         printf("%d = %d", i, sum);
   }
   printf("\n");
   return 0;
}

Output

When the above program is executed, it produces the following result −

enter 1st no of series: 3
enter total no's in series: 10
enter Common Difference: 5
sum of A.P series is: 3 + 8 + 13 + 18 + 23 + 28 + 33 + 38 + 43 + 48 = 255
enter 1st no of series: 2
enter total no's in series: 15
enter Common Difference: 10
sum of A.P series is: 2 + 12 + 22 + 32 + 42 + 52 + 62 + 72 + 82 + 92 + 102 + 112 + 122 + 132 + 142 = 1080