Resources for Geometric Sequences
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Questions
13
With Worked SolutionClick Here -
Video Tutorials
5
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HSC Questions
1
With Worked SolutionClick Here
Geometric Sequences Theory
![The general term of a geometric sequence is \(T_n=a r^{n-1}\) where \(a\) is the first term, \(n\) is the number of terms and \(r\) is the common ratio.\\ \begin{multicols}{2} \textbf{Example}\\ %24650 A geometric series has a second term 4.5 and the ratio of the fourth term to the third term is 1.5. \begin{itemize}[leftmargin=1.7em,nosep] \item[\bf{i)}]Find the common ratio \(r\) \item[\bf{ii)}]What is the first term \(a\)? \end{itemize} \textbf{Solution} \begin{itemize}[leftmargin=1.7em,nosep] \item[\bf{i)}] \(\begin{aligned}[t] &\text{The common ratio is given as}\\ &r=\frac{T_{n}}{T_{n-1}}=\frac{T_{4}}{T_{3}}=1.5 \end{aligned}\)\\ \item[\textbf{ii)}] \(\begin{aligned}[t] T_{n} &=a r^{n-1} \\ T_{2} &=a r=4.5 \\ a \times 1.5 &=4.5 \end{aligned}\)\\ \(\begin{aligned} &\therefore\ \text{the first term is 3} \end{aligned}\)\\ \end{itemize} \end{multicols}](/media/kopb43mm/4763.png)