Answer
$\$1710.34$
Work Step by Step
The provided sequence is $\$1000,\$1050,\$1102.50,\ldots$,
Therefore,
Find the common ratio $r$, by using the formula $r=\frac{{{a}_{2}}}{{{a}_{1}}}$.
$\begin{align}
& r=\frac{1050}{1000} \\
& =1.05
\end{align}$
The general formula is ${{a}_{n}}=a{{r}^{n-1}}$.
Substitute the value of the first term and the common ratio in the equation ${{a}_{n}}=a{{r}^{n-1}}$, where $n=12$.
$\begin{align}
& {{a}_{12\text{th}}}=1000{{\left( 1.05 \right)}^{12-1}} \\
& =1000{{\left( 1.05 \right)}^{11}}
\end{align}$
So, the value obtained is $1710.34$
Thus, the value of the $12\text{th}$ term of the geometric sequence $\$1000,\$1050,\$1102.50,\ldots$ is $\$1710.34$.
