Question

Classify the following set of numbers by determining which of the options is true.

3, 1, 1/3
, 1/9
, 1/27
, . . .

Option #1: The set is an arithmetic sequence.

Option #2: The set is a geometric sequence.

Option #3: The set is some other type of sequence.

Option #4: The set is not a sequence.

(1 point)

Answer 1

To determine the type of sequence represented by the numbers 3, 1, 1/3, 1/9, 1/27, we need to analyze the pattern of the numbers.

1. **Arithmetic Sequence**: In an arithmetic sequence, the difference between consecutive terms is constant. In this case:
- 1 - 3 = -2
- 1/3 - 1 = -2/3
- 1/9 - 1/3 = -2/9
- 1/27 - 1/9 = -2/27
Clearly, the differences are not constant, so this is not an arithmetic sequence.

2. **Geometric Sequence**: In a geometric sequence, the ratio between consecutive terms is constant. Let's find the ratios:
- 1 / 3 = 1/3
- (1/3) / 1 = 1/3
- (1/9) / (1/3) = 1/3
- (1/27) / (1/9) = 1/3
The ratio between each pair is constant at 1/3. Thus, this is a geometric sequence.

Since the sequence has constant ratios, we conclude that:

**Option #2: The set is a geometric sequence.**