Answer
The \[{{n}^{th}}\] term of given geometric sequence is \[{{a}_{n}}={{10}^{3-n}}\]. The eighth term of the geometric sequence is\[\frac{1}{100,000}\].
Work Step by Step
Here, the first term is \[{{a}_{1}}=100\] and the ratio is,
\[\begin{align}
& r=\frac{{{a}_{2}}}{{{a}_{1}}} \\
& =\frac{10}{100} \\
& =\frac{1}{10}
\end{align}\]
Hence, the general term for the given geometric sequence is
\[\begin{align}
& {{a}_{n}}={{a}_{1}}{{r}^{n-1}} \\
& \,\,\,\,\,\,=100{{\left( \frac{1}{10} \right)}^{n-1}}\,\, \\
\end{align}\]
To find the eighth term put \[n=8\] in the above formula, to get:
\[\begin{align}
& {{a}_{8}}={{a}_{1}}{{r}^{8-1}} \\
& =100\cdot {{\left( \frac{1}{10} \right)}^{7}} \\
& =100\cdot \frac{1}{10000000} \\
& =\frac{1}{100000}
\end{align}\]
The \[{{n}^{th}}\] term of given geometric sequence is \[{{a}_{n}}={{10}^{3-n}}\]. The eighth term of the geometric sequence is\[\frac{1}{100,000}\].
