Answer
The \[{{n}^{th}}\] term of given geometric sequence is \[{{a}_{n}}={{2}^{n-1}}\]. The eighth term of the geometric sequence is\[128\].
Work Step by Step
Here, the first term is \[{{a}_{1}}=1\] and the ratio is,
\[\begin{align}
& r=\frac{{{a}_{2}}}{{{a}_{1}}} \\
& =\frac{2}{1} \\
& =2
\end{align}\]
Hence, the general term for the given geometric sequence is
\[\begin{align}
& {{a}_{n}}={{a}_{1}}{{r}^{n-1}} \\
& \,\,\,\,\,\,=1.{{(2)}^{n-1}} \\
& \,\,\,\,\,\,={{2}^{n-1}} \\
\end{align}\]
To find the eighth term put \[n=8\] in the above formulae, to get:
\[\begin{align}
& {{a}_{8}}={{a}_{1}}{{r}^{8-1}} \\
& =1\cdot {{2}^{7}} \\
& =1\cdot 128 \\
& =128
\end{align}\]
The \[{{n}^{th}}\] term of given geometric sequence is \[{{a}_{n}}={{2}^{n-1}}\]. The eighth term of the geometric sequence is\[128\].
