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# geometric series

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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.

Mar 13, 2021

### 2+0 Answers

#1
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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!

Mar 13, 2021
#2
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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   Mar 13, 2021