Question

Create an explicit formula to represent the number of bacteria in a petri dish, which is shown by the sequence {200, 120, 72, 43.2, 25.92, …}

Answer 1

`a_n=200(0.6)^(n-1)`

Explanation:

The explicit formula for a geometric sequence is
`a_n=a_1(r)^(n-1)` where
`a_n` is the
`n`th term,
`a_1` is the first term, and
`r` is the common ratio.

Here, the common ratio is
`r=0.6` because
`(120)/(200)=0.6`,
`(72)/(120)=0.6`, and so on. We also know that our first term is
`a_1=200`, thus, our explicit formula for the geometric sequence is
`a_n=200(0.6)^(n-1)`