Question

write an equation to describe the sequence below, and then find the 4th term. use n to represent the position of a term in the sequence, where n = 1 for the first term. 24, 72, 216, ... write your answer using decimals and integers. a_n = ( )^{n - 1} a_4 =

Explanation:

Step1: Identify the sequence type

This is a geometric sequence as $\frac{72}{24}=3$ and $\frac{216}{72}=3$. The general formula for a geometric sequence is $a_n=a_1r^{n - 1}$, where $a_1$ is the first - term and $r$ is the common ratio.

Step2: Determine $a_1$ and $r$

Here, $a_1 = 24$ and $r = 3$. So the equation for the sequence is $a_n=24\times3^{n - 1}$.

Step3: Find the 4th term

Substitute $n = 4$ into the formula $a_n=24\times3^{n - 1}$. Then $a_4=24\times3^{4 - 1}=24\times3^3=24\times27 = 648$.

Answer:

$a_n = 24(3)^{n - 1}$
$a_4 = 648$