QuestionIdentify the sequence type: $2, 4, 16, \ldots$ - is it arithmetic, geometric, or neither?

Studdy Solution

STEP 1

Assumptions1. The sequence given is $,4,16, \ldots$ . We need to determine if this sequence is arithmetic, geometric, or neither.

STEP 2

First, let's recall the definitions of arithmetic and geometric sequences.An arithmetic sequence is a sequence of numbers in which the difference between any two successive members is a constant. This means that if we subtract any term from the term that follows it, we should always get the same number.
A geometric sequence is a sequence of numbers in which the ratio of any two adjacent terms is constant. This means that if we divide any term by the term that precedes it, we should always get the same number.

STEP 3

Let's first check if the sequence is arithmetic. We do this by subtracting each term from the term that follows it.
$-2 =2$ $16 - =12$

STEP 4

We can see that the differences between the terms are not constant. Therefore, the sequence is not arithmetic.

STEP 5

Now, let's check if the sequence is geometric. We do this by dividing each term by the term that precedes it.
$\frac{4}{2} =2$ $\frac{16}{4} =4$

STEP 6

We can see that the ratios between the terms are not constant. Therefore, the sequence is not geometric.

STEP 7

Since the sequence is neither arithmetic (the differences between terms are not constant) nor geometric (the ratios between terms are not constant), the answer is "neither".
The sequence $2,4,16, \ldots$ is neither an arithmetic sequence nor a geometric sequence.

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QuestionIdentify the sequence type: $2, 4, 16, \ldots$ - is it arithmetic, geometric, or neither?

Studdy Solution

STEP 1

Assumptions1. The sequence given is $,4,16, \ldots$ . We need to determine if this sequence is arithmetic, geometric, or neither.

STEP 2

STEP 3

Let's first check if the sequence is arithmetic. We do this by subtracting each term from the term that follows it.
$-2 =2$ $16 - =12$

STEP 4

We can see that the differences between the terms are not constant. Therefore, the sequence is not arithmetic.

STEP 5

Now, let's check if the sequence is geometric. We do this by dividing each term by the term that precedes it.
$\frac{4}{2} =2$ $\frac{16}{4} =4$

STEP 6

We can see that the ratios between the terms are not constant. Therefore, the sequence is not geometric.

STEP 7

Since the sequence is neither arithmetic (the differences between terms are not constant) nor geometric (the ratios between terms are not constant), the answer is "neither".
The sequence $2,4,16, \ldots$ is neither an arithmetic sequence nor a geometric sequence.

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QuestionIdentify the sequence type: 2,4,16,…2, 4, 16, \ldots2,4,16,… - is it arithmetic, geometric, or neither?

Studdy Solution

STEP 1

Assumptions1. The sequence given is ,4,16,…,4,16, \ldots,4,16,… . We need to determine if this sequence is arithmetic, geometric, or neither.

STEP 2

STEP 3

Let's first check if the sequence is arithmetic. We do this by subtracting each term from the term that follows it.−2=2 -2 =2−2=216−=1216 - =1216−=12

STEP 4

We can see that the differences between the terms are not constant. Therefore, the sequence is not arithmetic.

STEP 5

Now, let's check if the sequence is geometric. We do this by dividing each term by the term that precedes it.42=2\frac{4}{2} =224​=2164=4\frac{16}{4} =4416​=4

STEP 6

We can see that the ratios between the terms are not constant. Therefore, the sequence is not geometric.

STEP 7

Since the sequence is neither arithmetic (the differences between terms are not constant) nor geometric (the ratios between terms are not constant), the answer is "neither".The sequence 2,4,16,…2,4,16, \ldots2,4,16,… is neither an arithmetic sequence nor a geometric sequence.

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QuestionIdentify the sequence type: $2, 4, 16, \ldots$ - is it arithmetic, geometric, or neither?

Assumptions1. The sequence given is $,4,16, \ldots$ . We need to determine if this sequence is arithmetic, geometric, or neither.

Let's first check if the sequence is arithmetic. We do this by subtracting each term from the term that follows it.
$-2 =2$ $16 - =12$

Now, let's check if the sequence is geometric. We do this by dividing each term by the term that precedes it.
$\frac{4}{2} =2$ $\frac{16}{4} =4$

Since the sequence is neither arithmetic (the differences between terms are not constant) nor geometric (the ratios between terms are not constant), the answer is "neither".
The sequence $2,4,16, \ldots$ is neither an arithmetic sequence nor a geometric sequence.