Determine the 18th term of the sequence 3,9,27,...

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:

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:

To find the 18th term, substitute 18 for n. So:

Subtract:

Evaluate:

Multiply:

And we're done!