What kind of sequence is this? 101, 89, 77, 65, ... 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: 101, 89, 77, 65, ... Are the consecutive differences in the sequence equal? 89 - 101 = -12, 77 - 89 = -12, 65 - 77 = -12. 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. 89 / 101 ≈ 0.881188, 77 / 89 ≈ 0.865169, 65 / 77 ≈ 0.844156. 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? $\newline$ $101, 89, 77, 65, \dots$ $\newline$ 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

101, 89, 77, 65, \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: $101, 89, 77, 65, \ldots$ Are the consecutive differences in the sequence equal? $\newline$ $89 - 101 = -12$ , $77 - 89 = -12$ , $65 - 77 = -12$ . $\newline$ 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. $\newline$ $\frac{89}{101} \approx 0.881188$ , $\frac{77}{89} \approx 0.865169$ , $\frac{65}{77} \approx 0.844156$ . $\newline$ 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.