SOLUTION: find the ninth term of the sequence 2,6,18,54....using the formula a n=1 x r (n-1)

Question 119215: find the ninth term of the sequence 2,6,18,54....using the formula a n=1 x r (n-1)
Found 2 solutions by jim_thompson5910, stanbon:
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 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 n=0, then

if n=1, then

if n=2, then

etc...

Now to find the 9th term, plug in n=8 (since we started at zero n=8 is the 9th term)

Raise 3 to the 8th power to 6,561

Multiply 2 and 6,561 to get 13,122

So the 9th term is 13,122
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find the ninth term of the sequence 2,6,18,54....using the formula a(n)=a(1) x r^(n-1)
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The sequence is a geometric sequence with a(1) = 2, and r = 6/2=3
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Formula: a(n) = (a(1))*r^(n-1)
a(9) = 2*3^(8)
a(9) = 13,122
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Cheers,
Stan H.
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