user input in c - c

Question

I cannot figure out how to take away a letter dependent on user input. For example, if I enter b the code should output cdefghijklmno... If I enter c the code should output defghijklmno... I just don't know where to do the math?
#include <stdio.h>
int main(void) {
char letter;
printf("Type one letter of alphabet and following letters will appear (lowercase): ");
scanf_s("%c", &letter);
if (letter >= 'a' && letter <= 'z'){
printf("%c, valid entry!\n\n", letter);
for (letter = 'a'; letter <= 'z'; ++letter){
printf("%c ", letter);
}
} else {
printf("%c, invalid entry.\n\n", letter);
}
return 0;
}

Answer 1

In this line:
for (letter = 'a'; letter <= 'z'; ++letter){
why do you start at a? Dont you want to start one after the user input letter, which is stored in letter?
So do that:
for (++letter; letter <= 'z'; ++letter){

Answer 2

if I enter b the code should output cdefghijklmno... If I enter c the code should output defghijklmno... I just don't know where to do the math
As #Ben has suggested, change your for loop to :
for (++letter; letter <= 'z'; ++letter)
{
printf("%c ", letter);
}
The reason of using ++letter is to print the alphabets which come after the entered letter up to z
This would do the job
further, from OP's comment:
To give the user repeated chances if input is incorrect
using a while loop would be helpful :
while( (scanf(" %c",&letter) == 1) && letter!='*')
{
if (letter >= 'a' && letter <= 'z')
{
printf("%c, valid entry!\n\n", letter);
for (++letter; letter <= 'z'; ++letter)
{
printf("%c ", letter);
}
printf("\n\n");
// break;
// place the above break if you want to stop scanning after first successful entry
}
else
{
printf("%c, invalid entry.\n", letter);
printf("try again\n\n");
}
}
this loop would continue till the use enters * (an asterik)
Note : while( (scanf(" %c",&letter) == 1) && letter!='*') here, we check whether scanf() successfully scanned or not and whether the scanned element is * or not
sample input :
1
2
a
t
3
*
output :
Type one letter of alphabet and following letters will appear (lowercase):
1, invalid entry.
try again
2, invalid entry.
try again
a, valid entry!
b c d e f g h i j k l m n o p q r s t u v w x y z
t, valid entry!
u v w x y z
3, invalid entry.
try again
*
ended

Answer 3

Try to increment the letter variable by 1 in for loop parameter:
for (letter += 1; letter <= 'z'; ++letter){
printf("%c ", letter);
}

Answer 4

You can also do it this way:
#include <stdio.h>
#include <ctype.h>
#define MAX 122
int
main(void) {
char letter;
int i;
printf("Type one letter of the alphabet(lowercase): ");
scanf("%c", &letter);
if (islower(letter)) {
printf("%c, valid entry!\n\n", letter);
for (i = letter + 1; i <= MAX; i++) {
printf("%c", i);
}
} else {
printf("%c, invalid entry.\n\n", letter);
}
return 0;
}