How to append strings using sprintf?

Question

You need:

sprintf(Buffer,"Hello World");
sprintf(Buffer + strlen(Buffer),"Good Morning");
sprintf(Buffer + strlen(Buffer),"Good Afternoon");

and of course you need your buffer to be big enough.

int length = 0;
length += sprintf(Buffer+length, "Hello World");
length += sprintf(Buffer+length, "Good Morning");
length += sprintf(Buffer+length, "Good Afternoon");

Here is a version with some resistance to errors. It is useful if you do not care when errors happen so long as you can continue along your merry way when they do.

int bytes_added( int result_of_sprintf )
{
    return (result_of_sprintf > 0) ? result_of_sprintf : 0;
}

int length = 0;
length += bytes_added(sprintf(Buffer+length, "Hello World"));
length += bytes_added(sprintf(Buffer+length, "Good Morning"));
length += bytes_added(sprintf(Buffer+length, "Good Afternoon"));

For safety (buffer overflow) I recommend to use snprintf()

const int MAX_BUF = 1000;
char* Buffer = malloc(MAX_BUF);

int length = 0;
length += snprintf(Buffer+length, MAX_BUF-length, "Hello World");
length += snprintf(Buffer+length, MAX_BUF-length, "Good Morning");
length += snprintf(Buffer+length, MAX_BUF-length, "Good Afternoon");

A snprintfcat() wrapper for snprintf():

size_t 
snprintfcat(
    char* buf,
    size_t bufSize,
    char const* fmt,
    ...)
{
    size_t result;
    va_list args;
    size_t len = strnlen( buf, bufSize);

    va_start( args, fmt);
    result = vsnprintf( buf + len, bufSize - len, fmt, args);
    va_end( args);

    return result + len;
}

Use the return value of sprintf()

Buffer += sprintf(Buffer,"Hello World");
Buffer += sprintf(Buffer,"Good Morning");
Buffer += sprintf(Buffer,"Good Afternoon");

Why do you want to use sprintf for string concatenation when there are methods intended specifically for what you need such as strcat and strncat?

I think you are looking for fmemopen(3):

#include <assert.h>
#include <stdio.h>

int main(void)
{
    char buf[128] = { 0 };
    FILE *fp = fmemopen(buf, sizeof(buf), "w");

    assert(fp);

    fprintf(fp, "Hello World!\n");
    fprintf(fp, "%s also work, of course.\n", "Format specifiers");
    fclose(fp);

    puts(buf);
    return 0;
}

If dynamic storage is more suitable for you use-case you could follow Liam's excellent suggestion about using open_memstream(3):

#include <assert.h>
#include <stdio.h>
#include <stdlib.h>

int main(void)
{
    char *buf;
    size_t size;
    FILE *fp = open_memstream(&buf, &size);

    assert(fp);

    fprintf(fp, "Hello World!\n");
    fprintf(fp, "%s also work, of course.\n", "Format specifiers");
    fclose(fp);

    puts(buf);
    free(buf);
    return 0;
}