Answer
(a) $S_n=S_{n-1}+2000=S_1+2000(n-1)$
(b) $S_5=38000$
Work Step by Step
(a) Step 1. The starting salary is $S_1=30000$,
Step 2. With a raise of $2000$ every year, his salary in second year will be $S_2=S_1+1\times2000$,
Step 3. His salary in third year will be $S_3=S_2+2000=S_1+2\times2000$ ... ...
Step 4. Repeat the above process, his salary in $n$th year will be $S_n=S_{n-1}+2000=S_1+2000(n-1)$
(b) In his fifth year, with $n=5$, we can get $S_5=38000$ as shown in the figure where his salaries up to 12 years have been calculated.
