Mathematics, 26.01.2020 16:31 mariaramirez110379
Find the 10th term in the following geometric sequence 1/3,1,3,9
Answers: 3
![\bf \cfrac{1}{3}~~,~~\stackrel{\frac{1}{3}(3)}{1}~~,~~\stackrel{1(3)}{3}~~,~~\stackrel{3(3)}{9}~~...\qquad \qquad \impliedby \textit{3 is the common ratio} \\\\[-0.35em] ~\dotfill](/tpl/images/0471/5022/49ee7.png)
![\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ r=3\\ a_1=\frac{1}{3}\\ n=10 \end{cases}\implies a_{10}=\cfrac{1}{3}\left(3^{10-9} \right) \\\\\\ a_{10}=\cfrac{1}{3}\cdot 3^9\implies a_{10}=\cfrac{1}{3}\cdot 19683\implies a_{10}=6561](/tpl/images/0471/5022/3733b.png)
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Find the 10th term in the following geometric sequence 1/3,1,3,9...
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