Question

write an equation to describe the sequence below, and then find the 5th term. use n to represent the position of a term in the sequence, where n = 1 for the first term. -173, -173/2, -173/4, ... write your answer using proper fractions, improper fractions, and integers. a_n = ( )^{n - 1} a_5 =

Explanation:

Step1: Identify the first - term and common ratio

The first - term $a_1=-173$, and the common ratio $r=\frac{-\frac{173}{2}}{-173}=\frac{1}{2}$.

Step2: Write the general formula for a geometric sequence

The general formula for a geometric sequence is $a_n=a_1r^{n - 1}$. Substituting $a_1=-173$ and $r = \frac{1}{2}$, we get $a_n=-173(\frac{1}{2})^{n - 1}$.

Step3: Find the 5th term

Substitute $n = 5$ into the formula $a_n=-173(\frac{1}{2})^{n - 1}$. Then $a_5=-173(\frac{1}{2})^{5 - 1}=-173\times\frac{1}{16}=-\frac{173}{16}$.

Answer:

$a_n=-173(\frac{1}{2})^{n - 1}$
$a_5=-\frac{173}{16}$