a(n)=(3)/(2)(-2)^(n-1) What is the 3^("rd ") term in the sequence?

Step 1: Understand sequence formula: Understand the sequence formula and identify the term to find. The sequence is defined by the formula a(n)=(3)/(2)(-2)^(n-1). We need to find the 3rd term, which means we will substitute n with 3 in the formula.Step 2: Substitute n with 3: Substitute n with 3 in the sequence formula. a(3)=(3)/(2)(-2)^(3-1)Step 3: Calculate the exponent: Calculate the exponent part of the formula. (-2)^(3-1) = (-2)^2Step 4: Evaluate the exponent: Evaluate the exponent. (-2)^2 = 4Step 5: Multiply by the coefficient: Multiply the result of the exponentiation by the coefficient. (3/2) * 4 = 3 * 2 = 6Step 6: Final answer: Write down the final answer. The 3rd term in the sequence is 6.

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a(n)=(3)/(2)(-2)^(n-1)
What is the
3^("rd ") term in the sequence?

$a(n)=\frac{3}{2}(-2)^{n-1}$ $\newline$ What is the $3^{\text {rd }}$ term in the sequence?

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Full solution

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

\newline

What is the

3^{\text {rd }}

term in the sequence?

Step $1$ : Understand sequence formula: Understand the sequence formula and identify the term to find. $\newline$ The sequence is defined by the formula $a(n)=\frac{3}{2}(-2)^{n-1}$ . We need to find the $3^{\text{rd}}$ term, which means we will substitute $n$ with $3$ in the formula.
Step $2$ : Substitute $n$ with $3$ : Substitute $n$ with $3$ in the sequence formula. $a(3)=\frac{3}{2}(-2)^{3-1}$
Step $3$ : Calculate the exponent: Calculate the exponent part of the formula. $(-2)^{(3-1)} = (-2)^2$
Step $4$ : Evaluate the exponent: Evaluate the exponent. $\newline$ $(-2)^2 = 4$
Step $5$ : Multiply by the coefficient: Multiply the result of the exponentiation by the coefficient. $\newline$ $(\frac{3}{2}) \times 4 = 3 \times 2 = 6$
Step $6$ : Final answer: Write down the final answer. $\newline$ The $3^{\text{rd}}$ term in the sequence is $6$ .