Suppose that we use the bisection algorithm to approximate $r=\sqrt{20}$ which the greatest zero of the function $f(x)= x^2 - 20 .$ We begin by finding two numbers, say, $a_1=4$ and $b_1= 5$ which bracket the zero. This is because $f(a_1)<0$ and $f(b_1)>0.$ Then we find $m_1 = (a_1+b_1)/2 =4.5$ and $h_1 = (b_1 - a_1)/2=0.5.$

We proceed with the bisection algorithm. Suppose that $a_n$ and $b_n$ bracket the zero. Then we compute $m_{n} = (a_n+b_n)/2$ and $h_n=|b_n-a_n|/2.$ If $f(m_{n})=0$ we stop because $r = m_{n}$ is the desired zero. If $f(m_n) > 0$ then $m_n$ becomes the new right endpoint, so we set $a_{n+1}:=a_n$ and $b_{n+1}:=m_n.$ If $f(m_n) < 0$ then $m_n$ becomes the new left endpoint, so we set $a_{n+1}:=m_n$ and $b_{n+1}:=b_n.$ Then $m_n$ is an approximation to $r$ with an error of $h_n$

Complete the following table:

$n$	$a_n$	$b_n$	$h_n$	$m_n$
$1$	$4$	$5$	$0.5$	$4.5$
$2$
$3$
$4$
$5$

Then is an approximation so far to $r$ with an error of .