[tex]\bf \textit{sum of an infinite geometric series}\\\\ S_n=\displaystyle\sum\limits_{i=0}^{\infty}\implies S_n=\cfrac{a_1}{1-r}~~ \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ S_n=60\\ r=\frac{1}{8} \end{cases} \\\\\\ 60=\cfrac{a_1}{~~1-\frac{1}{8}~~}\implies 60=\cfrac{a_1}{~~\frac{7}{8}~~}\implies 60=\cfrac{\frac{a_1}{1}}{~~\frac{7}{8}~~}\implies 60=\cfrac{8a_1}{7} \\\\\\ 420=8a_1\implies \cfrac{420}{8}=a_1\implies \cfrac{105}{2}=a_1[/tex]
