What kind of sequence is this? 161, 145, 129, 113, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: 161, 145, 129, 113, ... Are the consecutive differences in the sequence equal? 145 - 161 = -16, 129 - 145 = -16, 113 - 129 = -16. The consecutive differences in the sequence are equal.Identify Arithmetic Sequence: Since the consecutive differences are equal, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms.Check for Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. Given sequence: 161, 145, 129, 113, ... Are the ratios between consecutive terms in the sequence equal? 145 / 161 ≠ 129 / 145 ≠ 113 / 129. The ratios are not equal, so the sequence is not geometric.Final Conclusion: Based on the findings from the previous steps, we can conclude that the sequence is arithmetic because it has a common difference, and it is not geometric because it does not have a common ratio.

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What kind of sequence is this? $\newline$ $161, 145, 129, 113, \dots$ $\newline$ 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

161, 145, 129, 113, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: $161, 145, 129, 113, ext{...}$ Are the consecutive differences in the sequence equal? $145 - 161 = -16$ , $129 - 145 = -16$ , $113 - 129 = -16$ . The consecutive differences in the sequence are equal.
Identify Arithmetic Sequence: Since the consecutive differences are equal, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms.
Check for Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. Given sequence: $161, 145, 129, 113, ext{...}$ Are the ratios between consecutive terms in the sequence equal? $\frac{145}{161} \neq \frac{129}{145} \neq \frac{113}{129}$ . The ratios are not equal, so the sequence is not geometric.
Final Conclusion: Based on the findings from the previous steps, we can conclude that the sequence is arithmetic because it has a common difference, and it is not geometric because it does not have a common ratio.