Flex- Action Script programming Language

I'm surprised anyone's starting to learn ActionScript (assuming you're using it for Flash) when the rest of the planet is moving toward HTML5 but, to each their own :-)

The algorithm you want for that sequence is relatively simple, and should be simple to convert into any procedural language:

for limit = 5 to 1 inclusive, stepping by -1:
    for number = 1 to limit inclusive, stepping by 1:
        output number
    output newline

That's basically it. Based on my (very) limited exposure to AS3, that would come out as something like:

for (var lim:Number = 5; lim > 0, lim--) {
    for (var num:Number = 1; num <= lim, num++) {
        doSomethingWith(num);
    }
}

 var x:int = 5;
 while(x > 0) {
      var output:String = "";
      for(var i:int = x; i > 0; i--) {
          output = i + " " + output;
          x--;
      }
      trace(output);
 }

//Here the variable to build the string to "print"
var str:String="";

//We need two loops
//The first to change the row

for (var lim:int= 5; lim > 0; lim--) {

    //Reset the string each new row
    str="";

    //And here the scond to build the string to "print"
    for (var num:int= 1; num <= lim; num++) {
       str+=num+" ";
    }

    //Here "print" the string
    trace(str);
}

This is my code to create a pattern like that:

for (var i:int = 5; i >= 1; i--) { // represent the row
    trace("1"); // print first element
    for (var j:int = 2; j <= i; j++) { // represet the line
        trace(" " + j.toString()); // print space and a number
    }
    trace("\n"); //next line
}