SOLUTION: Find a general term a_n for the geometric sequence. a1=-1/7 r=6 show work

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Question 475308: Find a general term a_n for the geometric sequence.
a1=-1/7 r=6 show work
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Well look at the first four terms of the sequence:
-1%2F7,-6%2F7,-36%2F7...
Now notice you could factor out a common factor of -1%2F7 from each term.
Then the sequence would look like the following for n=1,2,3
n = 1, 2, 3 ...
An = 1, 6, 36 ...
establish a relationship and see if the pattern holds
1+=+6%5E0+=+6%5E%281-1%29+=+6%5E%28n-1%29
6+=+6%5E1+=+6%5E%282-1%29+=+6%5E%28n-1%29
36+=+6%5E2+=+6%5E%283-1%29+=+6%5E%28n-1%29
It does.
Therefore An = %28-1%2F7%29%2A6%5E%28n-1%29