## Geometric Sequences help

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
Dylicious
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Joined: Fri Jul 10, 2015 1:23 am
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### Geometric Sequences help

So I think I'm getting the general idea of them, however I feel like I'm spending an unnecessary amount of time guessing and checking for the common ratio. Particularly when the majority of the numbers in the sequence are fractions.

For example 27/64, 9/16, 3/4, 1, ?

Is there a trick for this or do I simply need to work on converting fractions quicker in my head?

buddy
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Joined: Sun Feb 22, 2009 10:05 pm
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### Re: Geometric Sequences help

I feel like I'm spending an unnecessary amount of time guessing and checking for the common ratio.
There isn't any guessing for common ratios. Just do the division and see if the answers match.
Particularly when the majority of the numbers in the sequence are fractions.

For example 27/64, 9/16, 3/4, 1, ?
Do the regular dividing. With fractions that means flip and multiply:

(9/16)/(27/64) = (9/16)*(64/27) = (9/27)*(64/16) = (1/3)*(4/1) = 4/3
(3/4)/(9/16) = (3/4)*(16/9) = (3/9)*(16/4) = (1/3)*(4/1) = 4/3
(1/1)/(3/4) = (1/1)*(4/3) = 4/3
r=4/3

or you could notice that 1*3/4 = 3/4, 3/4*3/4 = 9/16, 9/16*3/4 = 27/64. If you're multiplying by 3/4 going backwards then you're dividing by 4/3 going forwards.

Hope that helps.

Dylicious
Posts: 2
Joined: Fri Jul 10, 2015 1:23 am
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### Re: Geometric Sequences help

That helped a lot!
Thanks.