Question 1131338: find the nth term of a sequence whose first several terms are given -1/3, 1/9, -1/27, 1/81?
Answer by josgarithmetic(39614)   (Show Source):
You can put this solution on YOUR website! You can do this yourself. Obvious common ratio! Geometric Progression!  to reach each successive term.
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The terms alternate in sign; but Look at the denominators carefully:
3, 9, 27, 81, ...
What do you see? What is the pattern? How is this number changing to each next term? THAT tells you what you want to know.
Next, look at the alternating signs of the sequence.
Understand clearly, positive times negative is negative; and negative times negative is positive. Necessary to understand how signed numbers work.
FIRST TWO TERMS:
-1/3, 1/9
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How does the term,  occur based on the term  ?
You must expect R is a negative number.
-
So what is happening with the denominators?
 ;
and you can go on like this for the terms at index #2, and index #3.
If you do, you should see 
;
By now you must understand the pattern happening and can answer the question: What is the nth term of the sequence.
What is the common ratio between successive terms? Remember, it must be negative here:
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