Consider the following algorithm segment. Assume that $n$ is a positive integer.

for $i$:$=1to3n$

$s$:$=0$

for $j$:$=1toi-1$

$s$:$=s+j*(i-j+1)$

next $j$

$r$:$=s^2$

next $i$

It$"$ link.$)$

The number of operations is $$

$($b$)$ Apply the theorem on polynomial orders to the expression in part $($a$)$ to find that an order for the algorithm segment is $n$