c(n)=(4)/(9)(-3)^(n-1) What is the 3^("rd ") term in the sequence?

Identify term of sequence: Identify the term of the sequence we need to find. We are asked to find the 3rd term in the sequence defined by the formula c(n)=(4/9)(-3)^(n-1).Substitute term number: Substitute the term number into the formula. To find the 3rd term, we substitute n=3 into the formula c(n)=(4/9)(-3)^(n-1). c(3)=(4/9)(-3)^(3-1)Calculate the exponent: Calculate the exponent. Calculate the value of (-3)^(3-1), which is (-3)^2. (-3)^2 = 9Multiply by coefficient: Multiply the result of the exponentiation by the coefficient. Now, multiply the result from Step 3 by the coefficient (4/9). c(3)=(4/9)*9Simplify the expression: Simplify the expression. Simplify the multiplication to find the 3rd term. c(3)=(4/9)*9 = 4

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c(n)=(4)/(9)(-3)^(n-1)
What is the
3^("rd ") term in the sequence?

$c(n)=\frac{4}{9}(-3)^{n-1}$ $\newline$ What is the $3^{\text {rd }}$ term in the sequence?

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c(n)=\frac{4}{9}(-3)^{n-1}

\newline

What is the

3^{\text {rd }}

term in the sequence?

Identify term of sequence: Identify the term of the sequence we need to find. $\newline$ We are asked to find the $3^{\text{rd}}$ term in the sequence defined by the formula $c(n) = \left(\frac{4}{9}\right)(-3)^{n-1}$ .
Substitute term number: Substitute the term number into the formula. $\newline$ To find the $3^{\text{rd}}$ term, we substitute $n=3$ into the formula $c(n)=\left(\frac{4}{9}\right)(-3)^{(n-1)}$ . $\newline$ $c(3)=\left(\frac{4}{9}\right)(-3)^{(3-1)}$
Calculate the exponent: Calculate the exponent. $\newline$ Calculate the value of $(-3)^{(3-1)}$ , which is $(-3)^2$ . $\newline$ $(-3)^2 = 9$
Multiply by coefficient: Multiply the result of the exponentiation by the coefficient. $\newline$ Now, multiply the result from Step $3$ by the coefficient $(\frac{4}{9})$ . $\newline$ c( $3$ )=(\frac{ $4$ }{ $9$ })\times $9$
Simplify the expression: Simplify the expression. $\newline$ Simplify the multiplication to find the $3$ rd term. $\newline$ $c(3)=\left(\frac{4}{9}\right)*9 = 4$