`6,-2,2/3,-2/9,...` Write the next two apparent terms of the sequence. Describe the patterns used to find these terms.

Expert Answers
lemjay eNotes educator| Certified Educator

`6, -2, 2/3, -2/9`

To determine the next two terms, identify if it is an arithmetic or geometric sequence.

Take note that an arithmetic sequence has a common difference. While a geometric sequence have a common ratio.

To find the common difference, subtract the successive terms.




Since the three pairs of consecutive terms do not have the same result, the given sequence is not an arithmetic sequence.

To find the common ratio, divide the consecutive terms.


`(2/3)/(-2) = -1/3`


Since the result are the same, the given sequence is geometric. Its common ratio is `-1/3` .

So the 5th term of the geometric sequence is:

`-2/9*(-1/3) = 2/27`

And its 6th term is:


Therefore, the next two terms of the given sequence are `2/27` and `-2/81`.