What kind of sequence is this? 86, 103, 120, 137, ... 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: 86, 103, 120, 137, ... Are the consecutive differences in the sequence equal? Let's calculate: 103 - 86 = 17, 120 - 103 = 17, 137 - 120 = 17. 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: 103 / 86 ≈ 1.1977, 120 / 103 ≈ 1.1650, 137 / 120 ≈ 1.1417. 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? $\newline$ $86, 103, 120, 137, \dots$ $\newline$ 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

86, 103, 120, 137, \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: $86, 103, 120, 137, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? Let's calculate: $\newline$ $103 - 86 = 17$ , $\newline$ $120 - 103 = 17$ , $\newline$ $137 - 120 = 17$ . $\newline$ 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: $\newline$ $\frac{103}{86} \approx 1.1977$ , $\newline$ $\frac{120}{103} \approx 1.1650$ , $\newline$ $\frac{137}{120} \approx 1.1417$ . $\newline$ 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.