Answer
At the end of the ninth week, the student has $\$135$ in the student's account.
Work Step by Step
This is an arithmetic sequence since the same amount of money is deposited every week.
There is $\$30$ in the student's account the in second week and $\$45$ in the third week so we find the common difference $45-30=15$.
To find the amount of money in the first week subtract $\$15$ from $\$30$ to get $\$15$.
The common difference is $15$ and the starting amount is $15$ and you have to find the amount of money after $9$ weeks ($a_9$). Thus,
$a_{9}=a_{1}+(n-1)d$
$a_{9}=15+(9-1)15 $
$a_{9}=15+120 $
$a_{9}=135 $
There will be $\$135$ by the end of the ninth week
