What is the common ratio in the following geometric sequence?

2, 12
, 18
, 132
, . . .

(1 point)
Responses

−1.5
negative 1.5

12
Start Fraction 1 over 2 End Fraction

14
Start Fraction 1 over 4 End Fraction

4

1 answer

To find the common ratio of a geometric sequence, you divide any term by the previous term.

Let's calculate the common ratio using the given terms:

  1. From the first term (2) to the second term (12): \[ \text{Common Ratio (r)} = \frac{12}{2} = 6 \]

  2. From the second term (12) to the third term (18): \[ r = \frac{18}{12} = 1.5 \]

  3. From the third term (18) to the fourth term (132): \[ r = \frac{132}{18} = 7.3333\ldots \text{ (approximately)} \]

Since the ratios are not consistent, this sequence does not represent a geometric sequence, as a geometric sequence must have a constant common ratio.

However, if your question aims to ask about a certain meaningful term after calculations, the common ratio amongst the calculated would be 6 or 1.5, but not consistent.

None of the options reflect a valid constant ratio based on the provided terms, so please consider checking the terms or if it better fits a different series or pattern altogether.