[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}\\[-0.5em]
\hrulefill\\
n=7\\
S_7=44405\\
r=3.4
\end{cases}
\\\\[-0.35em]
~\dotfill [/tex]
[tex] \bf 44405=a_1\left( \cfrac{1-3.4^7}{1-3.4} \right)\implies 44405=a_1\left( \cfrac{-5251.3350144}{-2.4} \right)
\\\\\\
44405=a_1(2188.056256)\implies \cfrac{44405}{2188.056256}=a_1\implies 20.294268\approx a_1 [/tex]
