Math  /  Algebra

QuestionCarey is organizing her books and putting them on shelves. She put 2 books on the first shelf, 8 books on the second shelf, 32 books on the third shelf, and 128 books on the fourth shelf. What kind of sequence is this?

Studdy Solution

STEP 1

1. Carey is placing books on shelves in a specific pattern.
2. The number of books on each shelf follows a sequence.
3. The sequence type needs to be identified.

STEP 2

1. Identify the pattern in the sequence of numbers.
2. Determine the type of sequence based on the pattern.

STEP 3

List the number of books on each shelf: 2,8,32,1282, 8, 32, 128.

STEP 4

Observe the relationship between consecutive terms: - From 2 to 8: multiply by 4. - From 8 to 32: multiply by 4. - From 32 to 128: multiply by 4.

STEP 5

Since each term is obtained by multiplying the previous term by a constant (4), the sequence is a geometric sequence.
The sequence is a geometric sequence with a common ratio of 4.

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