Question:Sum of GP series in c programming language 

#include<stdio.h>
#include<math.h>

int main(){

    float a,r,i,tn;
    int n;
    float sum=0;

    printf("Enter the first number of the G.P. series: ");
    scanf("%f",&a);

    printf("Enter the total numbers in the G.P. series: ");
    scanf("%d",&n);

    printf("Enter the common ratio of G.P. series: ");
    scanf("%f",&r);

    sum = (a*(1 - pow(r,n+1)))/(1-r);
       tn = a * (1 -pow(r,n-1));

    printf("tn term of G.P.: %f",tn);
    printf("\nSum of the G.P.: %f",sum);

    return 0;
}
Sample output:
Enter the first number of the G.P. series: 1
Enter the total numbers in the G.P. series: 5
Enter the common ratio of G.P. series: 2
tn term of G.P. : 16.000000
Sum of the G.P. : 63.000000

Question:Sum of infinite GP series in c programming language 

#include<stdio.h>

int main(){

    float a,r;
    float sum=0;

    printf("Enter the first number of the G.P. series: ");
    scanf("%f",&a);

    printf("Enter the common ratio of G.P. series: ");
    scanf("%f",&r);

    if(1 > r)
         sum = a/(1-r);
    else
         sum = a/(r-1);

    printf("\nSum of the infinite G.P. series: %f",sum);

    return 0;
}
Sample output:
Enter the first number of the G.P. series: 1
Enter the common ratio of G.P. series: .5

Sum of the infinite G.P. series: 2.000000

Enter the first number of the G.P. series: 5
Enter the common ratio of G.P. series: 2

Sum of the infinite G.P. series: 5.000000

Question:Source code of simple bubble sort implementation using array ascending order in c programming language 

#include<stdio.h>
int main(){

  int s,temp,i,j,a[20];

  printf("Enter total numbers of elements: ");
  scanf("%d",&s);

  printf("Enter %d elements: ",s);
  for(i=0;i<s;i++)
      scanf("%d",&a[i]);

  //Bubble sorting algorithm
  for(i=s-2;i>=0;i--){
      for(j=0;j<=i;j++){
           if(a[j]>a[j+1]){
               temp=a[j];
              a[j]=a[j+1];
              a[j+1]=temp;
           }
      }
  }

  printf("After sorting: ");
  for(i=0;i<s;i++)
      printf(" %d",a[i]);

  return 0;
}
Sample Output:
Enter total numbers of elements: 5
Enter 5 elements: 6 2 0 11 9
After sorting:  0 2 6 9 11

Question:Source code of simple insertion sort implementation using array in ascending order in c programming language 

#include<stdio.h>
int main(){

  int i,j,s,temp,a[20];

  printf("Enter total elements: ");
  scanf("%d",&s);

  printf("Enter %d elements: ",s);
  for(i=0;i<s;i++)
      scanf("%d",&a[i]);

  for(i=1;i<s;i++){
      temp=a[i];
      j=i-1;
      while((temp<a[j])&&(j>=0)){
      a[j+1]=a[j];
          j=j-1;
      }
      a[j+1]=temp;
  }

  printf("After sorting: ");
  for(i=0;i<s;i++)
      printf(" %d",a[i]);

  return 0;
}
Sample Output:
Enter total elements: 5
Enter 5 elements: 3 7 9 0 2
After sorting:  0 2 3 7 9

Question:Source code of simple Selection sort implementation using array ascending order in c programming language 

#include<stdio.h>
int main(){

  int s,i,j,temp,a[20];

  printf("Enter total elements: ");
  scanf("%d",&s);

  printf("Enter %d elements: ",s);
  for(i=0;i<s;i++)
      scanf("%d",&a[i]);

  for(i=0;i<s;i++){
      for(j=i+1;j<s;j++){
           if(a[i]>a[j]){
               temp=a[i];
              a[i]=a[j];
              a[j]=temp;
           }
      }
  }

  printf("After sorting is: ");
  for(i=0;i<s;i++)
      printf(" %d",a[i]);

  return 0;
}
Sample Output:
Enter total elements: 5
Enter 5 elements: 4 5 0 21 7
The array after sorting is:  0 4 5 7 21

Question:Source code of simple quick sort implementation using array ascending order in c programming language 

#include<stdio.h>

void quicksort(int [10],int,int);

int main(){
  int x[20],size,i;

  printf("Enter size of the array: ");
  scanf("%d",&size);

  printf("Enter %d elements: ",size);
  for(i=0;i<size;i++)
    scanf("%d",&x[i]);

  quicksort(x,0,size-1);

  printf("Sorted elements: ");
  for(i=0;i<size;i++)
    printf(" %d",x[i]);

  return 0;
}

void quicksort(int x[10],int first,int last){
    int pivot,j,temp,i;

     if(first<last){
         pivot=first;
         i=first;
         j=last;

         while(i<j){
             while(x[i]<=x[pivot]&&i<last)
                 i++;
             while(x[j]>x[pivot])
                 j--;
             if(i<j){
                 temp=x[i];
                  x[i]=x[j];
                  x[j]=temp;
             }
         }

         temp=x[pivot];
         x[pivot]=x[j];
         x[j]=temp;
         quicksort(x,first,j-1);
         quicksort(x,j+1,last);

    }
}
Sample Output:
Enter size of the array: 5
Enter 5 elements: 3 8 0 1 2
Sorted elements: 0 1 2 3 8

Question:Source code of simple merge sort implementation using array in ascending order in c programming language 

#include<stdio.h>
#define MAX 50

void mergeSort(int arr[],int low,int mid,int high);
void partition(int arr[],int low,int high);

int main(){
   
    int merge[MAX],i,n;

    printf("Enter the total number of elements: ");
    scanf("%d",&n);

    printf("Enter the elements which to be sort: ");
    for(i=0;i<n;i++){
         scanf("%d",&merge[i]);
    }

    partition(merge,0,n-1);

    printf("After merge sorting elements are: ");
    for(i=0;i<n;i++){
         printf("%d ",merge[i]);
    }

   return 0;
}

void partition(int arr[],int low,int high){

    int mid;

    if(low<high){
         mid=(low+high)/2;
         partition(arr,low,mid);
         partition(arr,mid+1,high);
         mergeSort(arr,low,mid,high);
    }
}

void mergeSort(int arr[],int low,int mid,int high){

    int i,m,k,l,temp[MAX];

    l=low;
    i=low;
    m=mid+1;

    while((l<=mid)&&(m<=high)){

         if(arr[l]<=arr[m]){
             temp[i]=arr[l];
             l++;
         }
         else{
             temp[i]=arr[m];
             m++;
         }
         i++;
    }

    if(l>mid){
         for(k=m;k<=high;k++){
             temp[i]=arr[k];
             i++;
         }
    }
    else{
         for(k=l;k<=mid;k++){
             temp[i]=arr[k];
             i++;
         }
    }
   
    for(k=low;k<=high;k++){
         arr[k]=temp[k];
    }
}
Sample output:
Enter the total number of elements: 5
Enter the elements which to be sort: 2 5 0 9 1
After merge sorting elements are: 0 1 2 5 9

Question:C program to calculate factorial using recursion 

#include<stdio.h>
int fact(int);
int main(){
  int num,f;
  printf("\nEnter a number: ");
  scanf("%d",&num);
  f=fact(num);
  printf("\nFactorial of %d is: %d",num,f);
  return 0;
}

int fact(int n){
   if(n==1)
       return 1;
   else
       return(n*fact(n-1));
 }

Question:Find gcd of a number using recursion in c program 

#include<stdio.h>
int main(){
  int n1,n2,gcd;
  printf("\nEnter two numbers: ");
  scanf("%d %d",&n1,&n2);
  gcd=findgcd(n1,n2);
  printf("\nGCD of %d and %d is: %d",n1,n2,gcd);
  return 0;
}

int findgcd(int x,int y){
     while(x!=y){
          if(x>y)
              return findgcd(x-y,y);
          else
             return findgcd(x,y-x);
     }
     return x;
}

Question:Sum of digits in c using recursion 

#include<stdio.h>
int main(){
  int num,x;
  clrscr();
  printf("\nEnter a number: ");
  scanf("%d",&num);
  x=findsum(num);
  printf("Sum of the digits of %d is: %d",num,x);
  return 0;
}

int r,s;
int findsum(int n){
if(n){
         r=n%10;
         s=s+r;
         findsum(n/10);
     }
     else
       return s;
}