Suppose that we use Newton's Method to approximate $r=\sqrt[3]{120}$, which is the zero of the function $f(x)= x^3 - 120$. We begin with a good guess, say $x_1 = 6$. Then Newton's Method proceeds by the recursion $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$.

Compute the first few terms of the sequence $\lbrace x_n \rbrace$ obtained from Newton's method.

$x_1 = 6$

$x_2 =$
$x_3 =$
$x_4 =$
$x_5 =$
$x_6 =$
$x_7 =$