What kind of sequence is this? 53, 41, 29, 17, ... 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: 53, 41, 29, 17, ... Are the consecutive differences in the sequence equal? 41 - 53 = -12, 29 - 41 = -12, 17 - 29 = -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. 41 / 53 does not equal 29 / 41, and neither does it equal 17 / 29. Therefore, the sequence does not have a common ratio.Confirm Not Geometric Sequence: A geometric sequence requires a common ratio between consecutive terms, which this sequence does not have. Therefore, it is not a geometric sequence.

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What kind of sequence is this? $\newline$ $53, 41, 29, 17, \dots$ $\newline$ 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

53, 41, 29, 17, \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: $53, 41, 29, 17, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $41 - 53 = -12$ , $29 - 41 = -12$ , $17 - 29 = -12$ . $\newline$ 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. $\frac{41}{53}$ does not equal $\frac{29}{41}$ , and neither does it equal $\frac{17}{29}$ . Therefore, the sequence does not have a common ratio.
Confirm Not Geometric Sequence: A geometric sequence requires a common ratio between consecutive terms, which this sequence does not have. Therefore, it is not a geometric sequence.