What kind of sequence is this? 74, 59, 44, 29, ... 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: 74, 59, 44, 29, ... Are the consecutive differences in the sequence equal? 59 - 74 = -15, 44 - 59 = -15, 29 - 44 = -15. 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. 59 / 74 does not equal 44 / 59, nor does it equal 29 / 44. Therefore, the sequence does not have a common ratio.Final Sequence Classification: Since the sequence has a common difference but not a common ratio, it is an arithmetic sequence and not a geometric sequence.

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What kind of sequence is this? $\newline$ $74, 59, 44, 29, \dots$ $\newline$ 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

74, 59, 44, 29, \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: $74, 59, 44, 29, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $59 - 74 = -15$ , $44 - 59 = -15$ , $29 - 44 = -15$ . $\newline$ 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. $\frac{59}{74}$ does not equal $\frac{44}{59}$ , nor does it equal $\frac{29}{44}$ . Therefore, the sequence does not have a common ratio.
Final Sequence Classification: Since the sequence has a common difference but not a common ratio, it is an arithmetic sequence and not a geometric sequence.