What kind of sequence is this? 106, 97, 88, 79, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Verify Consecutive Differences Uniform: Let's verify if the differences between consecutive terms are uniform. Given sequence: 106, 97, 88, 79, ... Are the consecutive differences in the sequence equal? 97 - 106 = -9, 88 - 97 = -9, 79 - 88 = -9. 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. 97 / 106 = 0.915..., 88 / 97 = 0.907..., 79 / 88 = 0.897... The ratios between consecutive terms 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, but it is not geometric because it does not have a common ratio.

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What kind of sequence is this? $\newline$ $106, 97, 88, 79, ...$ $\newline$ 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

106, 97, 88, 79, ...

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Verify Consecutive Differences Uniform: Let's verify if the differences between consecutive terms are uniform. Given sequence: $106, 97, 88, 79, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $97 - 106 = -9$ , $88 - 97 = -9$ , $79 - 88 = -9$ . $\newline$ 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. $\newline$ $\frac{97}{106} = 0.915\ldots$ , $\frac{88}{97} = 0.907\ldots$ , $\frac{79}{88} = 0.897\ldots$ $\newline$ The ratios between consecutive terms 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, but it is not geometric because it does not have a common ratio.