What kind of sequence is this? 2, 8, 32, 128, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Arithmetic Sequence: To determine the type of sequence, we need to examine the relationship between consecutive terms. Let's first check if it's an arithmetic sequence by finding the difference between consecutive terms.Calculate Differences: The difference between the second term and the first term is 8 - 2 = 6. The difference between the third term and the second term is 32 - 8 = 24. Since the differences are not the same, the sequence is not arithmetic.Check Geometric Sequence: Now let's check if it's a geometric sequence by finding the ratio between consecutive terms.Calculate Ratios: The ratio between the second term and the first term is 8 / 2 = 4. The ratio between the third term and the second term is 32 / 8 = 4. The ratio between the fourth term and the third term is 128 / 32 = 4. Since the ratios are the same, the sequence is geometric.

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What kind of sequence is this? $\newline$ $2, 8, 32, 128, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Math Problems

Grade 8

Identify arithmetic and geometric sequences

Full solution

Q. What kind of sequence is this?

\newline

2, 8, 32, 128, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Arithmetic Sequence: To determine the type of sequence, we need to examine the relationship between consecutive terms. Let's first check if it's an arithmetic sequence by finding the difference between consecutive terms.
Calculate Differences: The difference between the second term and the first term is $8 - 2 = 6$ . The difference between the third term and the second term is $32 - 8 = 24$ . Since the differences are not the same, the sequence is not arithmetic.
Check Geometric Sequence: Now let's check if it's a geometric sequence by finding the ratio between consecutive terms.
Calculate Ratios: The ratio between the second term and the first term is $\frac{8}{2} = 4$ . The ratio between the third term and the second term is $\frac{32}{8} = 4$ . The ratio between the fourth term and the third term is $\frac{128}{32} = 4$ . Since the ratios are the same, the sequence is geometric.