SOLUTION: The first two terms of a geometric sequence are a(base1)=1/3 and a(base2)=1/6. How do I find a(base8) the eighth term?

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Question 175216: The first two terms of a geometric sequence are a(base1)=1/3 and a(base2)=1/6. How do I find a(base8) the eighth term?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The first two terms of a geometric sequence are a%5B1%5D=1%2F3 and a%5B2%5D=1%2F6. How do I find a%5B8%5D, the eighth term?

First find the common ratio, r, by dividing any term by
its preceding term.  So 



Now use the formula for the nth term:

matrix%281%2C4%2Ca%5Bn%5D%2C+%22=%22%2C+a%5B1%5D%2Cr%5E%28n-1%29%29 

Substitute n=8

matrix%281%2C3%2Ca%5B8%5D%2C+%22=%22%2C+a%5B1%5Dr%5E%288-1%29%29

matrix%281%2C3%2Ca%5B8%5D%2C+%22=%22%2C+a%5B1%5Dr%5E7%29

matrix%281%2C3%2Ca%5B8%5D%2C+%22=%22%2C+%281%2F3%29%281%2F2%29%5E7%29

matrix%281%2C3%2Ca%5B8%5D%2C+%22=%22%2C+%281%2F3%29%28%281%5E7%29%2F%282%5E7%29%29%29
            
matrix%281%2C3%2Ca%5B8%5D%2C+%22=%22%2C+%281%2F3%29%281%2F128%29%29

matrix%281%2C3%2Ca%5B8%5D%2C+%22=%22%2C+1%2F384%29

Edwin