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

Question 117751: 2, 6 , 18 , 54 , ....
In the sequence above what would be the 8th term?
Answer by jim_thompson5910(35256) (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

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

Now divide the 4th term 54 by the 3rd term 18 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 .

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

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

Notice if we let n=0, we get

notice this is the first term

and if we let n=1, we get

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)

Plug in n=7 and simplify

So the eighth term is 4,374

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