Answer
The nth term of the sequence described in Exercise 1 is given by the formula ${{a}_{n}}=\underline{{{a}_{1}}{{r}^{n-1}}}$, where ${{a}_{1}}$ is the first term and r is the common ratio of the equence.
Work Step by Step
The geometric sequence is a sequence in which each term after the first is obtained by multiplying the preceding term by a fixed nonzero constant.
Assume the sequence,
$1,2,4,8,16\ldots $
The common ratio between two consecutive terms in the above sequence is constant.
For example,
$\begin{align}
& \frac{2}{1}=\frac{4}{2} \\
& =\frac{8}{4} \\
& =\frac{16}{8} \\
& =2
\end{align}$
So, the common ration is a fixed nonzero constant that is 2 in this case.
Therefore, the $n$ th term (general term) of a geometric sequence is given by the formula,
${{a}_{n}}={{a}_{1}}{{r}^{n-1}}$
In this formula, ${{a}_{1}}$ is the first term and $ r $ is the common ratio of the sequence.
