program to get sum of 1 to 10 natural numbers.

//program to get sum of 1 to 10 natural numbers.
#include<stdio.h>
#include<conio.h>
void main()
{
int k=1,sum=0;   //initialization
printf("enter value of 'n'\n");
scanf("%d",&n);
while(k<=n)
   {
      sum=sum+k;
      k++;
   }
printf("the sum=%d,",sum);
getch();
}

note:
here I have used 'n' as an input. We  can input any value, may be 10 or 20 or 100.
If you want to use 10 in loop directly then you can use and there would be no input(no scanf(..))

program to print/display 1,11,111,1111,11111,.... to nth term.

//program to print/display 1,11,111,1111,11111,.... to nth term.
#include<stdio.h>
#include<conio.h>
#include<math.h>
void main()
{
int k=1,m=1,n;
printf("enter value of 'n'\n");
scanf("%d",&n);
while(m<=n)
   {
      printf("%d\n",k);
      
      k=k+pow(10,m);
      m++;
   }
getch();
}

logic applied:

1,11,111,1111...
can be written as
1,10+1,100+11,1000+111....
can be written as
1,10 ¹+1,10 ²+11,10 ³+111
converting it into formula
k=k+pow(10,m);

program to print/display 1,6,11,16....nth term.

//program to print/display 1,6,11,16....nth term.
#include<stdio.h>
#include<conio.h>
void main()
{
int k=1,n;
printf("enter value of 'n'\n");
scanf("%d",&n);
while(k<=n)
   {
      printf("%d,",k);
      k=k+5;
   }
getch();
}

program to display multiplication table of a number .

//program to display multiplication table of a number .
#include<stdio.h>
#include<conio.h>
void main()
{
int k=1,n;
printf("enter value of 'n'(as a number)\n");
scanf("%d",&n);
while(k<=10)
   {
      printf("%d*%d=%d\n",n,k,n*k);
      k++;
   }
getch();
}
-------------------------------- note:
1)You can directly print instead given format.
put
printf("%d\n",n*k);

2) you can use nested loop for this as well.
 like
for(i=1;i<=1;i++)
  {
    for(k=1;k<=10;k++)
      {
          printf("%d\n",i*k);
       }
   }
you can put i =n if you enter this.
------------------------------------------------------------------------------
let's see the program using nested loop
//program to display multiplication table of a number using nested loop.
#include<stdio.h>
#include<conio.h>
void main()
{
int k,n;
printf("enter value of 'n'(a number for multiplication table)\n");
scanf("%d",&n);
for(i=n;i<=n;i++)
  {
    for(k=1;k<=10;k++)
      {
          printf("%d\n",i*k);
       }
          printf("\n");
   }
getch();
}
-----------------------------------------------------------------------------------------
let's see the program to get multiplication table of numbers using nested loop
//program to display multiplication table of  numbers using nested loop.
#include<stdio.h>
#include<conio.h>
void main()
{
int k,n;
printf("for how many numbers, you want t o go for multiplication table\n");
scanf("%d",&n);                       // from 1 to n
for(i=1;i<=n;i++)
  {
    for(k=1;k<=10;k++)
      {
          printf("%d\n",i*k);
       }
          printf("\n");
   }
getch();

}