Find the common ratio and write out the first four terms of the geometric sequence $(1.09)^{n-1}$
Common ratio is
\[
\begin{array}{l}
a_{1}= \\
a_{2}= \\
a_{3}= \\
a_{4}=
\end{array}
\]
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Answer
\(\boxed{\text{The common ratio is } 1.09 \text{ and the first four terms of the geometric sequence are } 1.0, 1.09, 1.1881, \text{ and } 1.29503}\)
Step 1 ：Define the common ratio as \(r = 1.09\)
Step 2 ：Calculate the first term as \(a_{1} = r^{1-1} = 1.0\)
Step 3 ：Calculate the second term as \(a_{2} = r^{2-1} = 1.09\)
Step 4 ：Calculate the third term as \(a_{3} = r^{3-1} = 1.1881\)
Step 5 ：Calculate the fourth term as \(a_{4} = r^{4-1} = 1.29503\)
Step 6 ：\(\boxed{\text{The common ratio is } 1.09 \text{ and the first four terms of the geometric sequence are } 1.0, 1.09, 1.1881, \text{ and } 1.29503}\)
