Another geometric question
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Another geometric question

[From: ] [author: ] [Date: 11-06-08] [Hit: ]
an=a1*[(r)^n-1] With r being the common ratio and a1 being your first term.So for the 20th term,......
I thought I understood this and there was a question earlier and I guessed at the right answer, but I need to know exactly how to do this. Take the geometric sequence: 9, 18, 36, 72,... Write a rule for the nth term and then use the rule to find the 20th term.
Thanks a bunch if you could show the steps.

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First find the common ratio:

18/9 = 2

36/18 = 2

72/36 = 2

Therefore the common ratio or r=2

And so the general formula is

a_n = (a_1)r^(n-1)

And for this sequence the rule would be

a_n = (9)2^(n-1)

And then to compute the 20th term

a_20 = (9)2^(20-1)

= (9)2^19

= 4718592

:)

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Okay, So you need to order all the terms, Which you've done. Next, you divide them into each other to find the common ratio. This would be 18/9 = 2. 36/18 = 2. 72/36 = 2. This is r.
The basic look for a geometric series equation is
an=a1*[(r)^n-1] With r being the common ratio and a1 being your first term.
So for the 20th term, You would just plug everything in
a20=9*[(2)^20-1]
a20=9*524288
a20=4718592
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