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

Question

3, 1, 13 , 19 , 127 , . . .

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)
The true statement is Option #
.

Answer 1

To determine the type of sequence the numbers form (3, 1, 13, 19, 127), let's analyze them.

1. Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant.

   • The differences are:
     • 1 - 3 = -2
     • 13 - 1 = 12
     • 19 - 13 = 6
     • 127 - 19 = 108
   • Since the differences are not constant, this is not an arithmetic sequence.

2. Geometric Sequence: In a geometric sequence, the ratio of consecutive terms is constant.

   • The ratios are:
     • 1 / 3 = 1/3
     • 13 / 1 = 13
     • 19 / 13 ≈ 1.461538
     • 127 / 19 ≈ 6.684211
   • Since the ratios are not constant, this is not a geometric sequence.

3. Other Type of Sequence: Since it is not arithmetic or geometric, it may be some other type of sequence. In this case, we have different numbers that do not follow a simple identifiable pattern.

4. Not a Sequence: The set of numbers listed is indeed a sequence.

After analyzing the given numbers, we can conclude:

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