Question

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

4, 12, 36, ...

4 + 12 + 36 + ...

4 + 12 + 20 + ...

4, 12, 20, ...

Answer 1

4 + 12 + 36 + ...

Explanation:

4, 12, 36, ... is a geometric sequence, it has a common ratio of
`r=(36)/(12)=(12)/(4)=3`

When we add the terms of a geometric sequence we get a geometric series.

4+12+36+ ... is a geometric series, it has a common ratio of
`r=(36)/(12)=(12)/(4)=3`

4 + 12 + 20 + ... is not a geometric series because it has no common ratio

`(20)/(12)\\e (12)/(4)`

The second choice is correct