What kind of sequence is this? 11, 33, 99, 297, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Arithmetic Sequence: Let's first check if the sequence is an arithmetic sequence by finding the differences between consecutive terms. 11, 33, 99, 297, ... The differences are: 33 - 11 = 22 99 - 33 = 66 297 - 99 = 198Verify Differences: Now, let's check if these differences are the same (which is required for an arithmetic sequence). 22, 66, 198, ... The differences between these are: 66 - 22 = 44 198 - 66 = 132 These differences are not the same; therefore, the sequence is not arithmetic.Check Geometric Sequence: Next, let's check if the sequence is a geometric sequence by finding the ratios between consecutive terms. 11, 33, 99, 297, ... The ratios are: 33 / 11 = 3 99 / 33 = 3 297 / 99 = 3Verify Ratios: Now, let's check if these ratios are the same (which is required for a geometric sequence). 3, 3, 3, ... The ratios between consecutive terms are the same; therefore, the sequence is geometric.

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What kind of sequence is this? $\newline$ $11, 33, 99, 297, \dots$ $\newline$ 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

11, 33, 99, 297, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Arithmetic Sequence: Let's first check if the sequence is an arithmetic sequence by finding the differences between consecutive terms. $\newline$ $11, 33, 99, 297, \dots$ $\newline$ The differences are: $\newline$ $33 - 11 = 22$ $\newline$ $99 - 33 = 66$ $\newline$ $297 - 99 = 198$
Verify Differences: Now, let's check if these differences are the same (which is required for an arithmetic sequence). $\newline$ $22$ , $66$ , $198$ , ... $\newline$ The differences between these are: $\newline$ $66 - 22 = 44$ $\newline$ $198 - 66 = 132$ $\newline$ These differences are not the same; therefore, the sequence is not arithmetic.
Check Geometric Sequence: Next, let's check if the sequence is a geometric sequence by finding the ratios between consecutive terms. $\newline$ $11, 33, 99, 297, \dots$ $\newline$ The ratios are: $\newline$ $\frac{33}{11} = 3$ $\newline$ $\frac{99}{33} = 3$ $\newline$ $\frac{297}{99} = 3$
Verify Ratios: Now, let's check if these ratios are the same (which is required for a geometric sequence). $\newline$ $3, 3, 3, \ldots$ $\newline$ The ratios between consecutive terms are the same; therefore, the sequence is geometric.