Question

question what is a formula for the nth term of the given sequence? 12, 6, 3... answer $a_n = 24(2)^{n - 1}$ $a_n = 24(\frac{1}{2})^{n - 1}$ $a_n = 12(2)^{-n}$ $a_n = 12(2)^{1 - n}$

Explanation:

Step1: Identify the sequence type

The given sequence 12, 6, 3... is a geometric sequence since $\frac{6}{12}=\frac{1}{2}$ and $\frac{3}{6}=\frac{1}{2}$, with a common - ratio $r = \frac{1}{2}$.

Step2: Recall the formula for the nth term of a geometric sequence

The formula for the nth 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. Here, $a_{1}=12$ and $r=\frac{1}{2}$.

Step3: Substitute the values into the formula

$a_{n}=12\times(\frac{1}{2})^{n - 1}=12\times2^{1 - n}$.

Answer:

$a_{n}=12(2)^{1 - n}$