Given:
1, 3,9, 27, ...
To determine the 10th of the given geometric sequence, we use the formula:
[tex]a_n=a_1\cdot r^{n-1}[/tex]
where:
an=nth term of the sequence
r=common ratio
a1=first term of the sequence
We can get the common ratio by observing that:
Based on the given geometric sequence, we let:
n= 10
a1=1
r=3
We plug in what we know:
[tex]\begin{gathered} a_n=a_1\cdot r^{n-1} \\ a_{10}=1\cdot(3)^{10-1} \\ \text{Simplify} \\ a_{10}=1(3)^9 \\ a_{10}=19683 \end{gathered}[/tex]
Therefore, the 10th term of the given geometric sequence is 19683.
