SOLUTION: 2, 6 , 18 , 54 , .... In the sequence above what would be the 8th term?

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Question 117751: 2, 6 , 18 , 54 , ....
In the sequence above what would be the 8th term?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Notice that each term is increasing quickly. So this sequence might be a geometric sequence. To find out, let's simply divide the terms.

First divide the 2nd term 6 by the 1st term 2 to get
6%2F2=3

Now divide the 3rd term 18 by the 2nd term 6 to get
18%2F6=3

Now divide the 4th term 54 by the 3rd term 18 to get
54%2F18=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.

Now since we've started at 2, this means that a=2

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

a%5Bn%5D=2%2A3%5En


Notice if we let n=0, we get


a%5B0%5D=2%2A3%5E0=2%2A1=2 notice this is the first term


and if we let n=1, we get


a%5B1%5D=2%2A3%5E1=2%2A3=6 notice this is the second term


and this generates the sequence 2, 6 , 18 , 54 , ....


So to find the 8th term, let n=7 (remember, we started at n=0)


a%5B7%5D=2%2A3%5E7=2%2A2187=4374 Plug in n=7 and simplify



So the eighth term is 4,374