SOLUTION: find the 9th term of 1,3,9,27

Question 179479: find the 9th term of 1,3,9,27
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, let's find the formula (or rule) that ties all of these terms together:

Notice that each term is increasing exponentially (ie at a fast pace). So this sequence might be a geometric sequence. To find out, let's simply divide the terms.

First divide the 2nd term 3 by the 1st term 1 to get

Now divide the 3rd term 9 by the 2nd term 3 to get

Now divide the 4th term 27 by the 3rd term 9 to get

So if we pick any term and divide it by the previous term, we'll always get 3. This is the common ratio between the terms. So this means that . What this tells us is that to get the next term, simply multiply the current term by 3.

Now since we've started at 1, this means that

Since the general geometric sequence is , this means the sequence is

or simply where starts at

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Now let's find the 9th term.

The 9th term will occur when (since we started at )

Start with the given sequence

Plug in

Raise 3 to the 8th power to get 6,561

So the ninth term is

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