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

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Question 179479: find the 9th term of 1,3,9,27
Answer by jim_thompson5910(35256) About Me  (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
3%2F1=3

Now divide the 3rd term 9 by the 2nd term 3 to get
9%2F3=3

Now divide the 4th term 27 by the 3rd term 9 to get
27%2F9=3

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 r=3. 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 a=1

Since the general geometric sequence is a%5Bn%5D=ar%5En, this means the sequence is

a%5Bn%5D=1%2A3%5En or simply a%5Bn%5D=3%5En where n starts at n=0


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Now let's find the 9th term.


The 9th term will occur when n=8 (since we started at n=0)


a%5Bn%5D=3%5En Start with the given sequence


a%5B8%5D=3%5E8 Plug in n=8


a%5B8%5D=6561 Raise 3 to the 8th power to get 6,561


So the ninth term is a%5B8%5D=6561