What kind of sequence is this? 65, 58, 51, 44, ... 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: 65, 58, 51, 44, ... Are the consecutive differences in the sequence equal? 58 - 65 = -7, 51 - 58 = -7, 44 - 51 = -7. The consecutive differences in the sequence are equal and the common difference is -7.Check for Common Ratio: Since the sequence has a common difference, it could be an arithmetic sequence. Let's check if it could also be a geometric sequence by finding the ratios between consecutive terms. Are the ratios between consecutive terms in the sequence equal? 58 / 65 ≈ 0.8923, 51 / 58 ≈ 0.8793, 44 / 51 ≈ 0.8627. The ratios between consecutive terms are not equal.Identify Sequence Type: An arithmetic sequence has consecutive terms with a common difference, while a geometric sequence has consecutive terms with a common ratio. Since the given sequence has a common difference but not a common ratio, it is an arithmetic sequence.

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What kind of sequence is this? $\newline$ $65, 58, 51, 44, \dots$ $\newline$ 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

65, 58, 51, 44, \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: $65, 58, 51, 44, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $58 - 65 = -7$ , $51 - 58 = -7$ , $44 - 51 = -7$ . $\newline$ The consecutive differences in the sequence are equal and the common difference is $-7$ .
Check for Common Ratio: Since the sequence has a common difference, it could be an arithmetic sequence. Let's check if it could also be a geometric sequence by finding the ratios between consecutive terms. $\newline$ Are the ratios between consecutive terms in the sequence equal? $\newline$ $\frac{58}{65} \approx 0.8923$ , $\frac{51}{58} \approx 0.8793$ , $\frac{44}{51} \approx 0.8627$ . $\newline$ The ratios between consecutive terms are not equal.
Identify Sequence Type: An arithmetic sequence has consecutive terms with a common difference, while a geometric sequence has consecutive terms with a common ratio. Since the given sequence has a common difference but not a common ratio, it is an arithmetic sequence.