I have 3 HTML inputs. When modifying the text in input 1, input 2 should update with the text that was previously in input 1. Input 3 should similarly update with the text that was previously in input 2.

I have 3 HTML inputs. When modifying the text in input 1, input 2 should update with the text that was previously in input 1. Input 3 should similarly update with the text that was previously in input 2.

You can do it this way.
<input type="text" id="txt1" class="someclass" />
<input type="text" id="txt1" class="someclass" />
<input type="text" id="txt1" class="someclass" />
$('.someclass').change(function(){
$(this).next('.someclass').val($(this).val());
$(this).next('.someclass').change();
});
Binding keyup event will change as soon as you type something
Use the jQuery val() method to set the input values as desired.
<!doctype html>
<html>
<head>
<script type="text/javascript" src="jquery.min.js"></script>
<script type="text/javascript">
$(document).ready(function(){
$("#input1").keyup(function() {
$('#input2').val($('#input1').val());
$('#input3').val($('#input2').val());
});
});
</script>
</head>
<body>
<input type="text" id="input1" />
<input type="text" id="input2" />
<input type="text" id="input3" />
</body>
</html>