# C program to find the sum of arithmetic progression series

CServer Side ProgrammingProgramming

## 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−

Live Demo

#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