What kind of sequence is this? 142, 122, 102, 82, ... 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: 142, 122, 102, 82, ... Are the consecutive differences in the sequence equal? 122 - 142 = -20, 102 - 122 = -20, 82 - 102 = -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. 122 / 142 ≈ 0.8592, 102 / 122 ≈ 0.8361, 82 / 102 ≈ 0.8039. The ratios between consecutive terms are not equal.Confirm Not Geometric Sequence: 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? $\newline$ $142, 122, 102, 82, \dots$ $\newline$ 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

142, 122, 102, 82, \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: $142, 122, 102, 82, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $122 - 142 = -20$ , $102 - 122 = -20$ , $82 - 102 = -20$ . $\newline$ 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. $\newline$ $\frac{122}{142} \approx 0.8592$ , $\frac{102}{122} \approx 0.8361$ , $\frac{82}{102} \approx 0.8039$ . $\newline$ The ratios between consecutive terms are not equal.
Confirm Not Geometric Sequence: 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.