Question

Which of the following represents a geometric series (remember what a series is as opposed to a sequence)?

3 + 9 + 15 + ...

3 + 9 + 27 + ...

3, 9, 27, ...

3, 9, 15, ...

Answer 1

The first answer is correct

Answer 2

3 + 9 + 27 + ...

Explanation:

3 + 9 + 15 + ... is not a geometric series because it has no common ratio.

`(15)/(9)\\e (9)/(3)`

3 + 9 + 27 + ... is a geometric series because there is a common ratio;

`r=(27)/(9)=(9)/(3)=3`

3, 9, 27, ... is a geometric sequence and not a series. The sum of all the terms in a geometric sequence forms a geometric series.

3, 9, 15, ... is a not a geometric series.