(A) Find the Total Number of Additions and Multiplications That $\text { for } i:=1 \text { to } n$

Essay

(a) Find the total number of additions and multiplications that must be performed when the following algorithm is executed. Show your work carefully.
$\text { for } i:=1 \text { to } n$
$\text { for } j=i \text { to } n$
$a:=2 \cdot(5 \cdot i+j+1)$
$\text { next } j$
$\text { next } i$
(b) Find an order for the algorithm segment of part (a) 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.