What kind of sequence is this? 2, 4, 8, 16, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Differences Uniform: Step 1: Check if the differences between consecutive terms are uniform. Given sequence: 2, 4, 8, 16, ... Calculate the differences: 4 - 2 = 2, 8 - 4 = 4, 16 - 8 = 8. Check Ratios Consistent: Step 2: Check if the ratios between consecutive terms are consistent. Given sequence: 2, 4, 8, 16, ... Calculate the ratios: 4 / 2 = 2, 8 / 4 = 2, 16 / 8 = 2. Determine Sequence Type: Step 3: Determine the type of sequence. Since the differences are not the same (2, 4, 8), it's not arithmetic. The ratios are the same (2, 2, 2), indicating it's a geometric sequence.

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What kind of sequence is this? $\newline$ $2, 4, 8, 16, \ldots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Algebra 2

Classify formulas and sequences

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Q. What kind of sequence is this?

\newline

2, 4, 8, 16, \ldots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Differences Uniform: Step $1$ : Check if the differences between consecutive terms are uniform. Given sequence: $2, 4, 8, 16, \ldots$ Calculate the differences: $4 - 2 = 2$ , $8 - 4 = 4$ , $16 - 8 = 8$ .
Check Ratios Consistent: Step $2$ : Check if the ratios between consecutive terms are consistent. Given sequence: $2, 4, 8, 16, \ldots$ Calculate the ratios: $\frac{4}{2} = 2$ , $\frac{8}{4} = 2$ , $\frac{16}{8} = 2$ .
Determine Sequence Type: Step $3$ : Determine the type of sequence. Since the differences are not the same $2, 4, 8$ , it's not arithmetic. The ratios are the same $2, 2, 2$ , indicating it's a geometric sequence.