What kind of sequence is this? 69, 49, 29, 9, ... 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: 69, 49, 29, 9, ... Are the consecutive differences in the sequence equal? 49 - 69 = -20, 29 - 49 = -20, 9 - 29 = -20. 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: 69, 49, 29, 9, ... Are the ratios between consecutive terms in the sequence equal? 49 / 69 ≈ 0.7101, 29 / 49 ≈ 0.5918, 9 / 29 ≈ 0.3103. The ratios are not equal, so the sequence is not geometric.Final Conclusion: Since the sequence has a common difference but not a common ratio, it is an arithmetic sequence and not a geometric sequence. Therefore, the correct choice is (A) arithmetic.

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What kind of sequence is this? $\newline$ $69, 49, 29, 9, \ldots$ $\newline$ 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

69, 49, 29, 9, \ldots

\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: $69, 49, 29, 9, \ldots$ Are the consecutive differences in the sequence equal? $49 - 69 = -20$ , $29 - 49 = -20$ , $9 - 29 = -20$ . 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: $69, 49, 29, 9, \ldots$ Are the ratios between consecutive terms in the sequence equal? $\frac{49}{69} \approx 0.7101$ , $\frac{29}{49} \approx 0.5918$ , $\frac{9}{29} \approx 0.3103$ . The ratios are not equal, so the sequence is not geometric.
Final Conclusion: Since the sequence has a common difference but not a common ratio, it is an arithmetic sequence and not a geometric sequence. Therefore, the correct choice is $(A)$ arithmetic.