# Archimedes Numerical Roots

##### Age 16 to 18

Challenge Level

A sequence of numbers $x_1, x_2, x_3, ... ,$ starts with $x_1 = 2$,
and, if you know any term $x_n$, you can find the next term
$x_{n+1}$ using the formula $x_{n+1} = \frac{1}{2} \left( x_n +
\frac{3}{x_n} \right)$.