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.
+357 f(x)=x/3
f(x)=x/3+n
12+4=16
12+4+n=32
n=16
I'm kinda confused.
I think that's the answer.
Yay!
+128448 The common ratio of the first series is 4 / 12 =1/3 = r
The sum of the first series is 12 / ( 1 -r) = 12 /(1 - 1/3) = 12/ (2/3) = 12 (3/2) = 18
The common ratio of the second series is (4+ n) / 12 = r
And we know that in this series
12/ [ 1 - (4 + n) / 12 ] = 36 simplify
12 * 12 / [ 12 - 4 - n ] = 36
144 = 36 [ 8 - n ]
144 = 288 - 36n
36n = 288 -144
36n = 144
n = 144 / 36 = 4
Proof
Second series = (n + 4) /12 = (4 + 4) /12 = 8/12 = 2/3
Sum
12 / ( 1 - 2/3) =
12 / (1/3) =
12 (3/1) = 36
