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OpenStudy (anonymous):
9. What is the 10th term of the sequence 81, 27, 9, …
@timo86m
OpenStudy (anonymous):
Can you tell what the relation between the terms is?
OpenStudy (anonymous):
@Xavier its r=0.3333333333
OpenStudy (anonymous):
Why the repeating decimal? But yeah it's geometric with r=1/3. You can keep up the pattern to find the 10th term or use the general formula for a geometric sequence
OpenStudy (anonymous):
wait what?
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OpenStudy (anonymous):
is it 1/81
OpenStudy (anonymous):
@Xavier
OpenStudy (anonymous):
Write them all out and see if you have the 10th one
OpenStudy (anonymous):
Im not sure how to do that
OpenStudy (anonymous):
You have
81, 27, 9 so far. What is the next term?
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OpenStudy (anonymous):
@Xavier i continue to get 1/81 is that wrong...
OpenStudy (anonymous):
use geometric sequence
OpenStudy (anonymous):
http://en.wikipedia.org/wiki/Geometric_progression
81*r^1 = 27
^ first term
^ is a ratio you solve for
solving for r you get 1/3
now plug it back in
81*(1/3)^9=.0041152= 1/243
^ here we use 9 since the formula uses 0 for the first term and you want 10th.