Resources for Infinite Sum of a GP
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Questions
12
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Video Tutorials
3
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HSC Questions
4
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Infinite Sum of a GP Theory
![The sum to infinity of a geometric series is\\ \(S_{\infty}=\dfrac{a}{1-r}\), for \(-1<n<1\)\\ where \(a\) is the first term and \(r\) is the common nation.\\ \begin{multicols}{2} \textbf{Example}\\ %24686 The first term of a geometric series is 25 and the fourth term is \(\dfrac{1}{5}\) \begin{itemize} \item[\bf{i)}]Find the common ratio. \item[\bf{ii)}]Find the limiting sum of the series. \end{itemize} \columnbreak \textbf{Solution}\\ $\begin{aligned} \text{(i)}\quad a &=25, T_{4}=\frac{1}{5} \\ \frac{1}{5} &=25 \times r^{3} \\ r^{3} &=\frac{1}{125} \\ r&=\frac{1}{5}\\ \text { (ii) } \quad S_{\infty}&=\frac{25}{1-\frac{1}{5}} \\ S_{\infty}&=31.25 \end{aligned}$\\ \end{multicols}](/media/f3xl1osv/4767.png)