Single quotes will not parse PHP variables inside of them. Either use double quotes or use a dot to extend the echo.
$variableName = 'Ralph';
echo 'Hello '.$variableName.'!';
OR
echo "Hello $variableName!";
And in your case:
$i = 1;
echo '<p class="paragraph'.$i.'"></p>';
++i;
OR
$i = 1;
echo "<p class='paragraph$i'></p>";
++i;