Question

Find the 10thterm of the following geometric sequence,1, 3,9, 27, ...

Answer 1

Given:

1, 3,9, 27, ...

To determine the 10th of the given geometric sequence, we use the formula:

`a_n=a_1\cdot r^(n-1)`

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:

`\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}`

Therefore, the 10th term of the given geometric sequence is 19683.