Question

How do you find the 10th term in the geometric sequence 25, 5, 1, 0.2, ...?

Answer 1

Write an exponential equation.

Explanation:

Each term of the geometric sequence is `1/5` the previous term. Therefore, you can say that each term is the previous term multiplied by `5^-1`. We can write an equation that models this, starting at `25`, where `x` is the number term in the sequence.

`f(x)=25(5)^-(x-1)`

With this equation, the first term would be calculated so: `f(x)=25(5)^-(1-1)=25(5)^-0=25*1=25`

Finding the tenth term: `f(x)=25(5)^-(10-1)=25(5)^-9=25/(5^9)=(5^2)/(5^9)=color(blue)(1/(5^7))`.

This is equal to `color(red)(0.0000128)`.