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 three times that of the first series. Find the value of n.
1 - Sum up the first infinite series using the "Infinite Series formula"
2 - Whatever sum you get from (1) above, multiply it by 3 and that is the sum of the 2nd infinite series.
3 - Again, use the "infinite Sum Formula" to find n, bearing in mind that the "common ratio" of the 2nd series is:(4 + n) / 12. You should get n = 16 / 3
+128475 First series......common ratio between terms is 4/12 = 1/3
Sum of this series is represented by : 12 / [ 1 -1/3 ] = 12/ (2/3) = 18
The second series has a sum of 18 * 3 = 54
The common ratio is [4 + n] /12
So
12 / [ 1 - (4 +n)/12 ] = 54
12/54 = 1 - (4 + n) /12
2/9 = 1 - (4 + n) /12
-7/9 = - (4 + n) /12
12 (7/9) = 4 + n
84/9 - 4 = n
48/9 = n = 16/3 [just as the Guest found!!! ]
