Question

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

Answer 1

Answer:

$x_{18}=387420489$

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:

$x_n=a(r)^{n-1}$

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:

$x_n=3(3)^{n-1}$

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

$x_{18}=3(3)^{18-1}$

Subtract:

$x_{18}=3(3)^{17}$

Evaluate:

$x_{18}=3(129140163)$

Multiply:

$x_{18}=387420489$

And we're done!