Question

Find the 10th term in the following geometric sequence 1/3,1,3,9

Answer 1

19683

Explanation:

Answer 2

`\bf \cfrac{1}{3}~~,~~\stackrel{(1)/(3)(3)}{1}~~,~~\stackrel{1(3)}{3}~~,~~\stackrel{3(3)}{9}~~...\qquad \qquad \impliedby \textit{3 is the common ratio} \\\\[-0.35em] ~\dotfill`

`\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=(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`