What kind of sequence is this? 218, 199, 180, 161, ... 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: 218, 199, 180, 161, ... Are the consecutive differences in the sequence equal? 199 - 218 = -19, 180 - 199 = -19, 161 - 180 = -19. 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. 199 / 218 ≈ 0.9128, 180 / 199 ≈ 0.9045, 161 / 180 ≈ 0.8944. The ratios between consecutive terms are not equal.Conclusion: Since the sequence has a common difference but not a common ratio, it is an arithmetic sequence and not a geometric sequence.

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What kind of sequence is this? $\newline$ $218, 199, 180, 161, \dots$ $\newline$ 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

218, 199, 180, 161, \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: $218, 199, 180, 161, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $199 - 218 = -19$ , $180 - 199 = -19$ , $161 - 180 = -19$ . $\newline$ 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. $\frac{199}{218} \approx 0.9128$ , $\frac{180}{199} \approx 0.9045$ , $\frac{161}{180} \approx 0.8944$ . The ratios between consecutive terms are not equal.
Conclusion: Since the sequence has a common difference but not a common ratio, it is an arithmetic sequence and not a geometric sequence.