Mathematics, 23.06.2019 11:30 daniellecraig77
An infinite geometric series has common ratio 1/8 and sum 60. what is the first term of the series?
Answers: 1
![\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](/tpl/images/0007/7865/29b3f.png)
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An infinite geometric series has common ratio 1/8 and sum 60. what is the first term of the series?...
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