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 \( c(n) \):

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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