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Given the geometric sequence: 27 ; 9 ; 3 ...

  1. ​Determine a formula for $T_{n}$, the nth term of the sequence.
  2. Why does the sum to infinity for this sequence exist?
  3. Determine $S_{\infty}$

 

 

 

in Mathematics by Diamond (61,682 points) | 668 views

1 Answer

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1. r= 9/27 = 1/3

  a= 27

 Tn= 27.(1/3)^(n-1)

2. Its because r=-1<r<1  , which is r= 1/3

3. Sum to infinity= a/(1-r)=27/(1- 1/3)= 40.5
by Diamond (42,394 points)

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