Identify which of the sequences below is a geometric sequence. A. 2, 4, 6, 8, ... B. 3, 6, 18, 54, ... C. 2, 6, 18, 54, ... D. 2, 6, 18, 36, ...

C

Step-by-step explanation:

For a sequence to be a geometric sequence, each successive term has to be a multiple of the previous term. It has to be true and same for all of the terms.

Checking A):

we see that each term is gotten by adding 2 to the previous term. It is arithmetic series. For geometric series, a same number had to be multiplied, not added.

Checking B):

This doesn't follow the rule of any sequence. 6 is twice of 3, 18 is thrice of 6, & 54 is thrice of 18. Not all of them are same, so it is not a geometric sequence.

Checking C):

6 is three times 2, 18 is 3 times 6, & 54 is 3 times 18. So all of them are thrice the previous one. So it is a geometric seris.

Checking D):

We see that 6 is thrice of 2, 18 is thrice of 6 BUT 36 is NOT thrice of 18 (rather twice). So it doesn't follow rule of geometric sequence.

We see that C is the correct answer.