Question

c(n) = \frac{4}{9}(-3)^{n - 1}
what is the 3^rd term in the sequence?
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Explanation:

Step1: Identify the value of n

To find the 3rd term, we use \( n = 3 \) in the sequence formula \( c(n)=\frac{4}{9}(-3)^{n - 1} \).

Step2: Substitute n = 3 into the formula

Substitute \( n = 3 \) into \( c(n) \):
\[

$$\begin{align*} c(3)&=\frac{4}{9}(-3)^{3 - 1}\\ &=\frac{4}{9}(-3)^{2} \end{align*}$$

\]

Step3: Calculate \( (-3)^2 \)

We know that \( (-3)^2=(-3)\times(-3) = 9 \). So now the formula becomes:
\[
c(3)=\frac{4}{9}\times9
\]

Step4: Simplify the expression

The 9 in the numerator and the 9 in the denominator cancel out:
\[
c(3) = 4
\]

Answer:

4