+0  
 
0
38
1
avatar

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.

 Jul 5, 2021
 #1
avatar+120966 
+1

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

 

 

cool cool cool

 Jul 5, 2021

10 Online Users