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.
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
