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The first term of an infinite geometric sequence is 2. The sum of the sequence is 6. What is the common ratio of the sequence?

 Jan 4, 2015

Best Answer 

 #1
avatar+128079 
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The "formula" for the sum of an infinite sequence is given by

S = a0 / (1 - r)....where S is the sum, a0 is the initial value, and r is the common ratio...so we have...

6 = 2 / (1 - r)     mutiply both sides by 1-r

6(1 - r)  = 2        simplify

6 - 6r  = 2           rearrange

4 = 6r                solve for r

r = 2/3

 

 Jan 5, 2015
 #1
avatar+128079 
+5
Best Answer

The "formula" for the sum of an infinite sequence is given by

S = a0 / (1 - r)....where S is the sum, a0 is the initial value, and r is the common ratio...so we have...

6 = 2 / (1 - r)     mutiply both sides by 1-r

6(1 - r)  = 2        simplify

6 - 6r  = 2           rearrange

4 = 6r                solve for r

r = 2/3

 

CPhill Jan 5, 2015

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