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.

Guest Nov 22, 2020

#1**+1 **

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

Guest Nov 22, 2020

#2**+1 **

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!!! ]

CPhill Nov 22, 2020