# A geometric sequence is defined recursively by a_n = 15a_(n-1), the first term of the sequence is 0.0001, how do you find the explicit formula for the nth term of the sequence?

##### 1 Answer
Feb 21, 2016

The explicit formula for the ${n}^{t h}$ term of the given geometric series is $0.0001 \cdot {15}^{n - 1}$.

#### Explanation:

As the geometric sequence is defined recursively by a_n=15a_(n−1) and the first term of the sequence is $0.0001$, it is obvious that the ratio of a term divided by its preceding term is $15$, that if written in general form of geometric series $\left\{a , a r , a {r}^{2} , a {r}^{3} , \ldots .\right\}$, $a$ is $0.0001$ and $r = 15$.

As the ${n}^{t h}$ term of geometric series is $a {r}^{n - 1}$, hence the explicit formula for the ${n}^{t h}$ term of the given geometric series is $0.0001 \cdot {15}^{n - 1}$.