What kind of sequence is this? 67, 85, 103, 121, ... 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: 67, 85, 103, 121, ... Are the consecutive differences in the sequence equal? 85 - 67 = 18, 103 - 85 = 18, 121 - 103 = 18. 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. 85 / 67 ≈ 1.2687, 103 / 85 ≈ 1.2118, 121 / 103 ≈ 1.1748. The ratios between consecutive terms are not equal.Conclusion: Since the sequence does not have a common ratio, it is not a geometric sequence. A geometric sequence is defined by having a common ratio between consecutive terms.

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What kind of sequence is this? $\newline$ $67, 85, 103, 121, \dots$ $\newline$ 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

67, 85, 103, 121, \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: $67, 85, 103, 121, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $85 - 67 = 18$ , $103 - 85 = 18$ , $121 - 103 = 18$ . $\newline$ 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. $\frac{85}{67} \approx 1.2687$ , $\frac{103}{85} \approx 1.2118$ , $\frac{121}{103} \approx 1.1748$ . The ratios between consecutive terms are not equal.
Conclusion: Since the sequence does not have a common ratio, it is not a geometric sequence. A geometric sequence is defined by having a common ratio between consecutive terms.