1. Can the numbers in a geometric sequence go down?
Yes, if the common ratio is a fraction the terms will decrease.
2. What happens in a geometric sequence when the common ratio is negative?
Each term will change sign, that is the sequence will oscillate.
e.g. A sequence with first term of 3 and a common ratio of -2 will be 3, -6, 12, -24, 48, ...
3. Does the common ratio have to be the same between every pair of terms for a sequence to be a geometric sequence?
Yes.
4. What is the difference between a geometric series and an arithmetic series?
Each term of a geometric series is calculated by multiplying the previous term by a fixed amount whereas each term of an aritmetic series is calculated by adding a fixed amount to the previous term.
5. When does a geometric sequence have a sum to infinity?
When the common ratio is a positve or negative fraction less than 1.
i.e. -1 < r < 1
