# Evaluate: a_{n}=((-1)^n)/(-3^{n+1)}

## Expression: $a_n=\frac{ {\left( -1 \right)}^{n} }{ -{3}^{n+1} }$

To find the first term, substitute $1$ for $n$ into $a_n=\frac{ {\left( -1 \right)}^{n} }{ -{3}^{n+1} }$

$a_1=\frac{ {\left( -1 \right)}^{1} }{ -{3}^{1+1} }$

Simplify the expression

$a_1=\frac{ 1 }{ 9 }$

To find the next term, substitute $2$ for $n$ into $a_n=\frac{ {\left( -1 \right)}^{n} }{ -{3}^{n+1} }$

$a_2=\frac{ {\left( -1 \right)}^{2} }{ -{3}^{2+1} }$

Simplify the expression

$a_2=-\frac{ 1 }{ 27 }$

To find the next term, substitute $3$ for $n$ into $a_n=\frac{ {\left( -1 \right)}^{n} }{ -{3}^{n+1} }$

$a_3=\frac{ {\left( -1 \right)}^{3} }{ -{3}^{3+1} }$

Simplify the expression

$a_3=\frac{ 1 }{ 81 }$

To find the next term, substitute $4$ for $n$ into $a_n=\frac{ {\left( -1 \right)}^{n} }{ -{3}^{n+1} }$

$a_4=\frac{ {\left( -1 \right)}^{4} }{ -{3}^{4+1} }$

Simplify the expression

$a_4=-\frac{ 1 }{ 243 }$

To find the next term, substitute $5$ for $n$ into $a_n=\frac{ {\left( -1 \right)}^{n} }{ -{3}^{n+1} }$

$a_5=\frac{ {\left( -1 \right)}^{5} }{ -{3}^{5+1} }$

Simplify the expression

$a_5=\frac{ 1 }{ 729 }$

To find the next term, substitute $6$ for $n$ into $a_n=\frac{ {\left( -1 \right)}^{n} }{ -{3}^{n+1} }$

$a_6=\frac{ {\left( -1 \right)}^{6} }{ -{3}^{6+1} }$

Simplify the expression

$a_6=-\frac{ 1 }{ 2187 }$

The first six terms of the sequence are $\begin{array} { l }\frac{ 1 }{ 9 },& -\frac{ 1 }{ 27 },& \frac{ 1 }{ 81 },& -\frac{ 1 }{ 243 },& \frac{ 1 }{ 729 },& -\frac{ 1 }{ 2187 }\end{array}$

$\begin{array} { l }\frac{ 1 }{ 9 },& -\frac{ 1 }{ 27 },& \frac{ 1 }{ 81 },& -\frac{ 1 }{ 243 },& \frac{ 1 }{ 729 },& -\frac{ 1 }{ 2187 }\end{array}$

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