Question

How do you write the explicit formula for the following geometric sequence: -0.1, 0.03, -0.009, 0.0027, -0.00081, ...?

Answer 1

`n^(th)` term of given geometric series is `(-0.1)xx(-0.3)^(n-1)`

Explanation:

In the given geometric series

`{-0.1,0.03,-0.009,0.0027,-0.00081,......}`,

the first term is `-0.1` and common ratio is `0.03/(-0.1)=(-0.009)/0.03=0.0027/(-0.009)=(-0.00081)/0.0027=-0.3`

As the `n^(th)` term of a geometric series whose first term is `a` and common ratio is `r` is `axxr^(n-1)`

Hence `n^(th)` term of given geometric series is

`(-0.1)xx(-0.3)^(n-1)`