SOLUTION: What function represents the geometric sequence ( 3,15,75,375,...)?

Question 121106: What function represents the geometric sequence ( 3,15,75,375,...)?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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

First divide the 2nd term 15 by the 1st term 3 to get

Now divide the 3rd term 75 by the 2nd term 15 to get

Now divide the 4th term 375 by the 3rd term 75 to get

So if we pick any term and divide it by the previous term, we'll always get 5. This is the common ratio between the terms. So this means that .

Now since we've started at 3, this means that

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

Check:

Notice when n=0, then

and when n=1, then

and when n=2, then

and when n=3, then

and so on....
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