c(n)=-(9)/(2)(-(4)/(3))^(n-1) What is the 2^("nd ") 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 c(n)=-(9)/(2)(-(4)/(3))^(n-1). We need to find the second term, which means we will substitute n with 2 in the formula.Step 2: Substitute n with 2: Substitute n with 2 in the sequence formula. c(2)=-(9)/(2)(-(4)/(3))^(2-1)Step 3: Simplify the exponent: Simplify the exponent. Since 2-1 equals 1, the expression becomes: c(2)=-(9)/(2)(-(4)/(3))^1Step 4: Calculate the value of the term: Calculate the value of the term with the exponent applied. The expression simplifies to: c(2)=-(9)/(2)(-4/3)Step 5: Multiply the constants: Multiply the constants. Now we multiply -(9)/(2) by (-4/3): c(2)=-(9)/(2) * (-4/3) c(2)= (9*4)/(2*3) c(2)= 36/6Step 6: Simplify the fraction: Simplify the fraction to find the second term. c(2)= 36/6 equals 6.

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c(n)=-(9)/(2)(-(4)/(3))^(n-1)
What is the
2^("nd ") term in the sequence?

$c(n)=-\frac{9}{2}\left(-\frac{4}{3}\right)^{n-1}$ $\newline$ What is the $2^{\text {nd }}$ term in the sequence?

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c(n)=-\frac{9}{2}\left(-\frac{4}{3}\right)^{n-1}

\newline

What is the

2^{\text {nd }}

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 $c(n)=-\frac{9}{2}\left(-\frac{4}{3}\right)^{n-1}$ . We need to find the second term, which means we will substitute $n$ with $2$ in the formula.
Step $2$ : Substitute $n$ with $2$ : Substitute $n$ with $2$ in the sequence formula. $c(2) = -\frac{9}{2}\left(-\frac{4}{3}\right)^{2-1}$
Step $3$ : Simplify the exponent: Simplify the exponent. $\newline$ Since $2^{-1}$ equals $1$ , the expression becomes: $\newline$ $c(2)=-\frac{9}{2}\left(-\frac{4}{3}\right)^1$
Step $4$ : Calculate the value of the term: Calculate the value of the term with the exponent applied. $\newline$ The expression simplifies to: $\newline$ $c(2)=-\frac{9}{2}\left(-\frac{4}{3}\right)$
Step $5$ : Multiply the constants: Multiply the constants. $\newline$ Now we multiply $-(\frac{9}{2})$ by $(-\frac{4}{3})$ : $\newline$ $c(2)=-(\frac{9}{2}) \times (-\frac{4}{3})$ $\newline$ $c(2)= \frac{9 \times 4}{2 \times 3}$ $\newline$ $c(2)= \frac{36}{6}$
Step $6$ : Simplify the fraction: Simplify the fraction to find the second term. $c(2)= \frac{36}{6}$ equals $6$ .