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,

4 + 12 + 36 + ...

Step-by-step explanation:

4, 12, 36, ... is a geometric sequence, it has a common ratio of

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

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

The second choice is correct

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for