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, ...

Respuesta :

Answer:

4 + 12 + 36 + ...

Step-by-step explanation:

4, 12, 36, ... is a geometric sequence, it has a common ratio of [tex]r=\frac{36}{12}=\frac{12}{4}=3[/tex]

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 [tex]r=\frac{36}{12}=\frac{12}{4}=3[/tex]

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

[tex]\frac{20}{12}\ne \frac{12}{4}[/tex]

The second choice is correct