which formula can be used to describe the sequence? -3, $\frac{3}{5}$, -$\frac{3}{25}$, $\frac{3}{125}$…

which formula can be used to describe the sequence? -3, $\frac{3}{5}$, -$\frac{3}{25}$, $\frac{3}{125}$, -$\frac{3}{625}$\no $f(x)=-3(\frac{1}{5})^{x - 1}$\no $f(x)=-3(-\frac{1}{5})^{x - 1}$\no $f(x)=-\frac{1}{5}(3)^{x - 1}$\no $f(x)=-\frac{1}{5}(-3)^{x - 1}$

which formula can be used to describe the sequence? -3, $\frac{3}{5}$, -$\frac{3}{25}$, $\frac{3}{125}$, -$\frac{3}{625}$\no $f(x)=-3(\frac{1}{5})^{x - 1}$\no $f(x)=-3(-\frac{1}{5})^{x - 1}$\no $f(x)=-\frac{1}{5}(3)^{x - 1}$\no $f(x)=-\frac{1}{5}(-3)^{x - 1}$

Answer

Explanation:

Step1: Identify the first - term and common ratio

The first - term $a_1$ of the sequence $-3,\frac{3}{5},-\frac{3}{25},\frac{3}{125},-\frac{3}{625}$ is $a_1=-3$. To find the common ratio $r$, divide the second term by the first term: $r = \frac{\frac{3}{5}}{-3}=\frac{3}{5}\times(-\frac{1}{3})=-\frac{1}{5}$.

Step2: Recall the formula for a geometric sequence

The general formula for a geometric sequence is $f(x)=a_1r^{x - 1}$, where $a_1$ is the first - term and $r$ is the common ratio. Substitute $a_1=-3$ and $r = -\frac{1}{5}$ into the formula, we get $f(x)=-3\left(-\frac{1}{5}\right)^{x - 1}$.

Answer:

$f(x)=-3\left(-\frac{1}{5}\right)^{x - 1}$