Answer
$\$1423.31$
Work Step by Step
$\$1000,\$1040,\$1081.60,\ldots$,
We know that:
${{a}_{n}}=a,ar,a{{r}^{2}},a{{r}^{3}},\ldots $,
Thus,
The first term ${{a}_{1}}$ is $a=1000$, and the second term ${{a}_{2}}$ is $a_2=1040$.
Find the common ratio, $r$, by using the formula $r=\frac{{{a}_{2}}}{{{a}_{1}}}$.
$\begin{align}
& r=\frac{1040}{1000} \\
& =1.04
\end{align}$
Now substitute the value of the first term and the common ratio in the equation ${{a}_{n}}=a{{r}^{n-1}}$, where $n=10$,
$\begin{align}
& {{a}_{10\text{th}}}=1000{{\left( 1.04 \right)}^{10-1}} \\
& =1000{{\left( 1.04 \right)}^{9}}
\end{align}$
Thus, the value obtained is $1423.31$
Threfore, the value of the $10\text{th}$ term of the geometric sequence $\$1000,\$1040,\$1081.60,\ldots$ is $\$1423.31$.
