How do you write a formula for the general term (the nth term) of the geometric sequence 4, 12, 36, 108, 324, . . .?

Nov 11, 2015

${x}_{n} = 4 \cdot {3}^{n - 1}$

Explanation:

The general term of any geometric sequence $\left({x}_{n}\right)$ is given by

${x}_{n} = a {r}^{n - 1}$, where $a$ is the first term and $r$ is the common ratio defined as $r = {x}_{n + 1} / {x}_{n}$.

So in this case $a = 4$ and $r = \frac{21}{4} = 3$.

$\therefore {x}_{n} = 4 \cdot {3}^{n - 1}$