SOLUTION: Given the sequence 216,36,6,1... Answer the following: is this sequence arithmetic or geometric? Justify your answer. Write the recursive formula for this sequence and u

Algebra ->  Finance -> SOLUTION: Given the sequence 216,36,6,1... Answer the following: is this sequence arithmetic or geometric? Justify your answer. Write the recursive formula for this sequence and u      Log On


   

Question 870889: Given the sequence 216,36,6,1... Answer the following: is this sequence arithmetic or geometric? Justify your answer.




Write the recursive formula for this sequence and use it to find the 16th term.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Notice how

36/216 = 1/6
6/36 = 1/6
1/6 = 1/6

So the common ratio is 1/6. This is a geometric sequence. The recursive formula is

a%5Bn%5D+=+%28a%5Bn-1%5D%29%2A%281%2F6%29

alternatively, you can write that as


a%5Bn%5D+=+%28a%5Bn-1%5D%29%2F6


to achieve the same result. The explicit formula for the nth term is a%5Bn%5D=216%2A%281%2F6%29%5E%28n-1%29 where n starts at n=1


The 16th term is when n = 16, so...


a%5Bn%5D=216%2A%281%2F6%29%5E%28n-1%29


a%5B16%5D=216%2A%281%2F6%29%5E%2816-1%29


a%5B16%5D=216%2A%281%2F6%29%5E%2815%29


a%5B16%5D=216%2A%28%281%5E15%29%2F%286%5E15%29%29


a%5B16%5D=216%2A%281%2F470184984576%29


a%5B16%5D=216%2F470184984576


a%5B16%5D=1%2F2176782336


a%5B16%5D=0000000004594


The 16th term as a fraction is 1%2F2176782336


The 16th term as a decimal is 0.0000000004594 (there are 9 zeros to the right of the decimal point before you hit 4594)