Given the geometric series #1/6 + 1/36 + 1/216+ ...#, what is the common ratio #r#?

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Answer 1 · 2017-06-07T00:13:58

#1/6#

#r# is the common ratio in the geometric series--in other words, it is what you multiply the #n#th term to get the #n+1# term.

So,

#1/6r=1/36#

#r=1/6#

Answer 2 · 2017-06-07T00:16:29

#r = frac(1)(6)#

To find the common ratio of any geometric series, we must find the quotient of any two consecutive terms:

#Rightarrow r = frac(1)(36) div frac(1)(6)#

#Rightarrow r = frac(1)(36) times frac(6)(1)#

#therefore r = frac(1)(6)#

Therefore, the common ratio #r# of the geometric series is #frac(1)(6)#.