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.
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
