SOLUTION: 243;81;27;... please explain the sequence

Algebra ->  Sequences-and-series -> SOLUTION: 243;81;27;... please explain the sequence      Log On


   

Question 942795: 243;81;27;... please explain the sequence
Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Divide the successive term by the previous term,
243%2F81=3
81%2F27=3
So each term is divided by 3 or multiplied by %281%2F3%29,
a%5Bn%5D=243%2A%281%2F3%29%5E%28n-1%29
a%5Bn%5D=243%2A%281%2F3%29%5En%2A%281%2F3%29%5E%28-1%29
a%5Bn%5D=243%2A%281%2F3%29%5En%2A3
a%5Bn%5D=729%2A%281%2F3%29%5En

Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
to find each term, we divide by 3, a common ratio, from the previous term
243%2F3=81
81%2F3=27
so, next would be
27%2F3=9
9%2F3=3
3%2F3=1
1%2F3=1%2F3 and so on
we can model it 243, 81, 27,+9, 3,1... with the exponential function below:
a%5Bn%5D=3%5E%28-n%2B+6%29+ where n=1,+2, 3,4...
Check:
When n+=+1, which represents the first term, we get
a%5B1%5D=+3%5E%28-1%2B+6%29+=+3%5E5+=+243
When n+=+2, which represents the second term, we get
a%5B2%5D=3%5E%28-2%2B+6%29+=+3%5E4+=+81