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

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Question 121106: What function represents the geometric sequence ( 3,15,75,375,...)?
Answer by jim_thompson5910(35256) About Me  (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
15%2F3=5

Now divide the 3rd term 75 by the 2nd term 15 to get
75%2F15=5

Now divide the 4th term 375 by the 3rd term 75 to get
375%2F75=5

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 r=5.

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

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

a%5Bn%5D=3%2A5%5En



Check:

Notice when n=0, then

a%5B0%5D=3%2A5%5E0=3%2A1=3

and when n=1, then

a%5B1%5D=3%2A5%5E1=3%2A5=15


and when n=2, then

a%5B2%5D=3%2A5%5E2=3%2A25=75

and when n=3, then

a%5B3%5D=3%2A5%5E3=3%2A125=375

and so on....