his first payment will be 200 bucks, a₁ = 200, and he'd like to pay 1.2 times more on the next month, namely 1.2 is a multiplier or the "common ratio", thus his 30 payments are
[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
n=30
\end{cases}
\\\\\\
S_{30}=a_1\left( \cfrac{1-r^{30}}{1-r} \right)\impliedby \textit{first 30 payments}[/tex]
[tex]\bf S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
n=30\\
a_1=200\\
r=1.2
\end{cases}
\\\\\\
S_{30}=200\left(\cfrac{1-1.2^{30}}{1-1.2} \right)\impliedby \textit{sum of the first 30 payments}[/tex]
