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An infinite geometric series has a first term of 12 and a second term of 4. A second infinite geometric series has the same first term of 16, a second term of 2+n, and a sum of four times that of the first series. Find the value of n.

 Feb 2, 2022
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First sequence:

 

4 / 12 ==1 / 3 - this is the common ratio.

 

Sum==12 / [1  -  1/3]==12 / [2/3] ==18

 

Second sequence:

 

4 x 18 ==12 / [1 - R], solve for R

R ==5 / 6

 

Second term==12 x 5/6 ==10

n + 2 ==10 and n==10 - 2 ==8

 Feb 2, 2022

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