Question

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?

Answer 1

The explicit formula for the `n^(th)` term of the given geometric series is `0.0001*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 `{a, ar, ar^2, ar^3,....}`, `a` is `0.0001` and `r=15`.

As the `n^(th)` term of geometric series is `ar^(n-1)`, hence the explicit formula for the `n^(th)` term of the given geometric series is `0.0001*15^(n-1)`.