## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

The $n^{th}$ term of the geometric sequence is: $a_n=1 (3)^{n-1}$ and $a_8= 2187$
The $n^{th}$ term of the sequence is given by the formula: $a_n=a_1r^{n-1}$ where $r$=common ratio and $a_1$= the first term The common ratio of a geometric sequence is equal to the quotient of any term and the term before it: $\ r = \dfrac{a_n}{a_{n-1}}$ or, $r=\dfrac{a_2}{a_1}=\dfrac{3}{1}=3$ Therefore, the $n^{th}$ term of the geometric sequence is: $a_n=1 (3)^{n-1}$ Now, the 8th term can be computed by substituting $8$ for $n$: $a_8=1 (3)^{8-1}=1 \cdot (3)^{7}= 2187$