Question

1. write an equation for the nth term of the geometric sequence -3, 9, -27, ...

Explanation:

Step1: Identify the first - term and common ratio

The first - term $a_1=-3$. To find the common ratio $r$, divide the second term by the first term. $r=\frac{9}{-3}=-3$.

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

The formula for the nth term of a geometric sequence is $a_n=a_1r^{n - 1}$. Substitute $a_1=-3$ and $r = - 3$ into the formula.
$a_n=-3\times(-3)^{n - 1}$.
Using the rule of exponents $a^m\times a^n=a^{m + n}$, we can rewrite it as $a_n=(-3)^n$.

Answer:

$a_n=(-3)^n$