What kind of sequence is this? 54, 62, 70, 78, ... 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: 54, 62, 70, 78, ... Are the consecutive differences in the sequence equal? 62 - 54 = 8, 70 - 62 = 8, 78 - 70 = 8. 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 Ratios for Geometric Sequence: Let's also check the ratios between consecutive terms to see if it could also be a geometric sequence. Given sequence: 54, 62, 70, 78, ... Are the ratios between consecutive terms in the sequence equal? 62 / 54 ≈ 1.148, 70 / 62 ≈ 1.129, 78 / 70 ≈ 1.114. 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? $\newline$ $54$ , $62$ , $70$ , $78$ , ... $\newline$ 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

54

62

70

78

, ...

\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: $54, 62, 70, 78, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $62 - 54 = 8$ , $70 - 62 = 8$ , $78 - 70 = 8$ . $\newline$ 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 Ratios for Geometric Sequence: Let's also check the ratios between consecutive terms to see if it could also be a geometric sequence. Given sequence: $54, 62, 70, 78, \ldots$ $\newline$ Are the ratios between consecutive terms in the sequence equal? $\newline$ $\frac{62}{54} \approx 1.148$ , $\frac{70}{62} \approx 1.129$ , $\frac{78}{70} \approx 1.114$ . $\newline$ 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.