Question

question what is a formula for the nth term of the given sequence? 100, 20, 4... answer $a_n = 100(5)^{-n}$ $a_n = 100(\frac{1}{5})^{n - 1}$ $a_n = 100(\frac{1}{5})^{n}$ $a_n = 500(\frac{1}{5})^{n - 1}$ submit answer

Explanation:

Step1: Identify the sequence type

The sequence 100, 20, 4... is a geometric - sequence since $\frac{20}{100}=\frac{4}{20}=\frac{1}{5}$. The general formula for the $n$th term of a geometric sequence is $a_{n}=a_{1}r^{n - 1}$, where $a_{1}$ is the first - term and $r$ is the common ratio.

Step2: Determine $a_{1}$ and $r$

Here, $a_{1}=100$ (the first term of the sequence) and $r=\frac{1}{5}$ (the common ratio).

Step3: Substitute values into the formula

Substitute $a_{1}=100$ and $r = \frac{1}{5}$ into the formula $a_{n}=a_{1}r^{n - 1}$, we get $a_{n}=100(\frac{1}{5})^{n - 1}$.

Answer:

$a_{n}=100(\frac{1}{5})^{n - 1}$