Geometric sequence

If your sequence is 2, 4, 8, ...? Then the common ratio is ...
If not, can you upload the original question.

Its a famous sum, but the series is
2 + 4 + 8 + 16 + ... + 2^16
So the common ratio for the successive terms is ...? The obvious answer is the correct one.

2? But does the common ratio not have to be between |x|<1 or it that only for sum to infinity? Also why is the 1 negative?

* Yes, r=2.
* The |r|<1 condition is only for a sum to infinity as you say, as you want the sum to converge to a finite value, so the terms in the series must decay (exponentially/geometrically). When the series has a finite number of terms, you just use the (easy to derive) expression.
* When you say the 1 negative, do you mean on the numerator / denominator? If so, you can multiply the usual expression by -1/-1 (so multiply both the numerator and denominator by -1). Then both of the expressions are positve for this series.

Ohh so it doesn't matter if I use the other version?

Its a fraction, you can multiply numerator and denominator by anything (well non-zero and has to be same multiplier top and bottom).