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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 $S_{\infty}$

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## 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 (39,663 points)

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1 answer