(A) Consider the Following Algorithm Segment:
For $i:=1$ To $n$

(a) Consider the following algorithm segment:
for $i:=1$ to $n$
for $j:=1$ to $i$
$x:=5 \cdot i+8 \cdot j$
next $j$
next $i$
How many additions and multiplications are performed when the inner loop of this algorithm segment is executed? How many additions and multiplications are performed when the entire algorithm segment is executed?
(b) Find an order for this algorithm segment from among the following: $\log _ { 2 } n , n , n \cdot \log _ { 2 } n$ , $n ^ { 2 } , n ^ { 3 }$ , and $n ^ { 4 }$ . Give a reason for your answer.