SOLUTION: state whether each is a geometric sequence,if so what is the common ratio and the next three terms. 1)24,12,6,3... 2)1,1,2,3,5...

Algebra ->  Sequences-and-series -> SOLUTION: state whether each is a geometric sequence,if so what is the common ratio and the next three terms. 1)24,12,6,3... 2)1,1,2,3,5...      Log On


   

Question 83396: state whether each is a geometric sequence,if so what is the common ratio and the next three terms.
1)24,12,6,3...
2)1,1,2,3,5...
Answer by Mona27(45) About Me  (Show Source):
You can put this solution on YOUR website!
A geometric sequence is one in which each term is multiplied by a constant number (called the common ratio) to obtain the next term.
Ans so to find the common ratio you should divide any term in the sequence by the one before it.
1) The first one IS a geometric sequence, since 12%2F24=6%2F12=3%2F6 (i.e. same ratio) and this is the common ratio (1%2F2)
To find the next three terms you continue multiplying by the common ratio:
so these are: 3%2F2, 3%2F4, 3%2F8
2) This is not a geometric sequence, since the ratio between each two consecutive terms is not the same. (This one is actually called the Fibonnacci Sequence)