Answer
a) $32,000(1.05)^{n-1}$
b) $32,000; 33,600;35,280; 37,044;38,896.20;40,841.01;42,883.06;45,027.21$
Work Step by Step
The salary $\{A_n\}$ is a geometric sequence with the elements:
$$\begin{cases}
A_1=32,000\\
r=1+0.05=1.05.
\end{cases}$$
a) We determine the $n$th element of the sequence which is the salary in the $n$th year:
$$A_n=A_1r^{n-1}=32,000(1.05)^{n-1}.$$
b) Calculate the first $8$ terms of the sequence:
$$\begin{align*}
A_1&=32,000\\
A_2&=A_1r=32,000(1.05)^1=33,600\\
A_3&=A_1r^2=32,000(1.05)^2=35,280\\
A_4&=A_1r^3=32,000(1.05)^3=37,044\\
A_5&=A_1r^4=32,000(1.05)^4=38,896.20\\
A_6&=A_1r^5=32,000(1.05)^5=40,841.01\\
A_7&=A_1r^6=32,000(1.05)^6=42,883.06\\
A_8&=A_1r^7=32,000(1.05)^7=45,027.21.
\end{align*}$$
