Question

Dentify which of the following is a geometric sequence.

a)3, 12, 48, . . .
b)3, 1, , . . .
c)0, 1, 3, 9, . . .
d) 3, 6, 12, 21, . . .

Answer 1

The correct geometric sequence from the options given is option a) 3, 12, 48, ..., as each term is consistently multiplied by 4. The correct option is (a).

Step-by-step explanation:

The question asks us to identify which sequence is a geometric sequence from the provided options.

• Option a) 3, 12, 48, ... is a geometric sequence because each term is multiplied by the same factor to get to the next term (in this case, multiplication by 4).
• Option b) 3, 1, ... does not provide enough information to determine if it's geometric.
• Option c) 0, 1, 3, 9, ... is not a geometric sequence because the ratio of successive terms is not constant.
• Option d) 3, 6, 12, 21, ... is not a geometric sequence because there's no constant factor between terms.

Therefore, the correct answer is option a) 3, 12, 48, ... which represents a geometric sequence.

Answer 2

The geometric sequences in the options are a) 3, 12, 48, ... and c) 0, 1, 3, 9, ...

Step-by-step explanation:

A geometric sequence is a sequence where each term is found by multiplying the previous term by a constant ratio. Let's analyze each option:

a) 3, 12, 48, . . . In this sequence, each term is obtained by multiplying the previous term by 4. So, this is a geometric sequence.

b) 3, 1, . . . This sequence does not have a consistent ratio between terms. So, it is not a geometric sequence.

c) 0, 1, 3, 9, . . . In this sequence, each term is obtained by multiplying the previous term by 3. So, this is a geometric sequence.

d) 3, 6, 12, 21, . . . This sequence does not have a consistent ratio between terms. So, it is not a geometric sequence.

Therefore, the geometric sequences are options a) and c).