Answer:
[tex]x_{18}=387420489[/tex]
Step-by-step explanation:
So we have the sequence:
3, 9, 27...
First, note that this is a geometric sequence because each subsequent term not increasing linearly.
To find the 18th term, we can write an explicit formula.
The standard explicit formula for a geometric sequence is:
[tex]x_n=a(r)^{n-1}[/tex]
Where a is the initial term, r is the common ratio, and n is the nth term.
From the sequence, we can see that the initial term a is 3. The common ratio is 3 since each subsequent term is 3 times the previous term. So, substitute:
[tex]x_n=3(3)^{n-1}[/tex]
To find the 18th term, substitute 18 for n. So:
[tex]x_{18}=3(3)^{18-1}[/tex]
Subtract:
[tex]x_{18}=3(3)^{17}[/tex]
Evaluate:
[tex]x_{18}=3(129140163)[/tex]
Multiply:
[tex]x_{18}=387420489[/tex]
And we're done!
