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.
+129850 First series
First term = 12
Common ratio = 4/12 = 1/3 = r
Sum = 12 / ( 1 - 1/3) = 12/ (2/3) = 18
Second series
First term = 16
Common ratio ( 2 + n) /16
Sum = 16 / [ 1 - (2 + n)/16 ] = 72
Simplify
16 / [ (14 - n) / 16 ] = 72
256 / ( 14 - n) = 72
256 = 72 ( 14 - n)
256 = 1008 - 72n
72n = 1008 - 256
72n = 752
n = 752/72 = 94/9
