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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 12, a second term of 4 + n, and a sum of two times that of the first series. Find the value of n.

 Sep 19, 2021
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First GP:

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

Sum==12 / [1 - 1/3]==12 / (2/3) ==18 - sum total of the 1st GP

 

Second GP:

Sum x 2 ==12 / [1 - R]

18 x 2 ==12 /[1 - R], solve for R

R ==2/3 - this is the common ratio of the 2nd GP

2nd term ==[4 + n]==12 x 2/3

[4 + n] ==8

n ==8 - 4 ==4

 Sep 19, 2021

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