### C program to find the sum of n odd numbers starting from 1:

In this tutorial, we will learn how to find the total sum of first ’n’ odd numbers using a *C program*. For example , the sum of first 3 odd numbers is *1 + 3 + 5 = 9*. The user will enter the value of *n* and our program will find out the sum and print out the answer.
We will discuss two different ways to find out the sum.

### 1. Using a for or while loop :

We can find out the sum by using one *for* or *while* loop. The loop will run from *1* to *n* and for each number it will check if it is divisible by *2* or not. If not, means it is an odd number, so add it to a final sum variable. Finally, print out the result. The program will explain below each step how it works.

### 2. A better approach : By finding the sum of all n numbers with a difference between each numbers mathematically :

The mathematical formulae to find the sum of first *n* numbers starting from *a* with a difference *d* between each is :

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

For example, *sum of first 5 numbers starting from 3 _ with a difference between each _2* is :

```
//here n = 5, a = 3 , d = 2
(5/2)[2*3 + (5-1)*2]
= (5/2)[6 + 8]
= (5/2) * 14
= 35
```

Manually , we can verify it like :

```
3 + 5 + 7 + 9 + 11
= 15 + 20
= 35
```

Our problem is to find the sum of first *n* odd numbers starting from 1. In this case , *a = 1*, *d = 2* ( since the difference between two odd numbers is 2). So, if we put these values in the above formulae, it will become :

```
(n/2)[2*a + (n-1)*d]
= (n/2)[2*1 + (n-1)*2]
= (n/2)[2 + 2n - 2]
= (n/2) * 2n
= n*n
= n^2
```

That means the sum of first *n* odd number is square of *n*.

### C program explains above solutions :

In the C program below, we will explain you how to solve the problem using above two approaches. Let’a take a look :

```
#include
//4
int findUsingWhile(int n){
//5
int i = 1;
int sum = 0;
int totalOdd = 0;
//6
while(totalOdd != n){
if(i%2 != 0){
sum += i;
totalOdd++;
}
i++;
}
//7
return sum;
}
//8
int findUsingFor(int n){
//9
int i;
int sum = 0;
int totalOdd = 0;
//10
for(i=1; totalOdd != n;i++){
if(i%2 != 0){
sum += i;
totalOdd ++;
}
}
//11
return sum;
}
//12
int usingMathematics(int n){
return n*n;
}
int main(){
//1
int n;
//2
printf("Enter the value of 'n' : ");
scanf("%d",&n);
//3
printf("Total sum using while loop : %d\n",findUsingWhile(n));
printf("Total sum using for loop : %d\n",findUsingFor(n));
printf("Total sum mathematically : %d\n",usingMathematics(n));
}
```

### Explanation :

*The commented numbers in the above program denote the step number below :*

- Create one integer variable n to store the value of user input number.
- Ask the user to enter a number. Read and store it in
*n*. - Calculate the sum of first
*n*odd numbers by using one*for loop*, using one*while loop*and by using the mathematical function shown above. For each case, print out the result. All these results should be same. *findUsingWhile*function takes the value of*n*as parameter and it calculates the sum using one*while*loop.- Create one variable
*i*to use in the loop,*totalOdd*to total odd numbers found and*sum*to store the sum of all odd numbers. - Run one
*while loop*. It will run continuously till total number of odd numbers becomes equal to the input*n*. Inside the loop, check if current value of*i*is odd or not. If odd, add it to the sum and increment the value of*totalOdd*. For each iteration, increment the value of*i*means we are checking it for each numbers continuously. - After the loop is completed, return the value of
*sum*. *findUsingFor*is similar to the above function. It takes the value of*n*as input and calculates the sum using a*for loop*.- Create three variables similarly as explained in the above function.
- Similar to
*while*function above, this function runs one*for loop*to find out the sum. It will run from*i = 1*. Each time , value of*i*is increased by one. If the value of*totalOdd*becomes equal to*n*, this loop will end. Inside the loop, check if*i*is odd or even. If odd, add its value to the final sum and increment the value of*totalOdd*. - Finally, after the loop is completed, return the value of
*sum*. - This is the third approach. Simply return the value of
*n*n*. It should be the required sum as explained above.

### Sample Output :

```
Enter the value of 'n' : 9
Total sum using while loop : 81
Total sum using for loop : 81
Total sum mathematically : 81
Enter the value of 'n' : 1
Total sum using while loop : 1
Total sum using for loop : 1
Total sum mathematically : 1
Enter the value of 'n' : 3
Total sum using while loop : 9
Total sum using for loop : 9
Total sum mathematically : 9
Enter the value of 'n' : 11
Total sum using while loop : 121
Total sum using for loop : 121
Total sum mathematically : 121
```