Question

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( a(n) = \frac{3}{2}(-2)^{n - 1} )
what is the ( 3^{\text{rd}} ) term in the sequence?
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Explanation:

Step1: Identify the formula and n value

The sequence formula is \( a(n)=\frac{3}{2}(-2)^{n - 1} \), and we need the 3rd term, so \( n = 3 \).

Step2: Substitute n = 3 into the formula

Substitute \( n = 3 \) into \( a(n)=\frac{3}{2}(-2)^{n - 1} \):
\( a(3)=\frac{3}{2}(-2)^{3 - 1} \)

Step3: Simplify the exponent

Simplify the exponent \( 3 - 1 = 2 \):
\( a(3)=\frac{3}{2}(-2)^{2} \)

Step4: Calculate the power

Calculate \( (-2)^{2}=4 \):
\( a(3)=\frac{3}{2}\times4 \)

Step5: Multiply the fractions and integers

Multiply \( \frac{3}{2}\times4 \). \( 4\) can be written as \( \frac{4}{1} \), so \( \frac{3}{2}\times\frac{4}{1}=\frac{12}{2} = 6 \).

Answer:

6