Consider the following programming segment. Your answer must rely on a combination structure. Answers that use Sigma notation will not be accepted.

counter $=500$

for i $=4$ to $3$n do $\{$

counter $=$ counter $+9$

for j $=$ i$+1$ to n do $\{$

counter $=$ counter $+18$

$\}$

$\}$

$//$ assume n $>10$

a$)$ Determine the value that the variable counter has after the segment is executed. Provide your answer as a function of n $($i$.$e$.,$ a formula which depends on n$).$ Make sure to explain how$/$why the parts of the formula relate to counting.

b$)$ Evaluate your answer in part a$)$ for n $=50.$ Show the work

Then check this number by implementing the code in Java. Use the value n $=50$ and print the variable counter after the code execution. You must provide the screenshots of the implementation and output.

What do you conclude?