What kind of sequence is this? 27, 42, 57, 72, ... 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: 27, 42, 57, 72, ... Are the consecutive differences in the sequence equal? 42 - 27 = 15, 57 - 42 = 15, 72 - 57 = 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. 42 / 27 does not equal 57 / 42, and neither equals 72 / 57. Therefore, the sequence does not have a common ratio and is not a geometric sequence.Final Conclusion: Based on the findings from the previous steps, the sequence is not geometric but is arithmetic because it has a common difference. Therefore, the correct choice is: (A) arithmetic.

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What kind of sequence is this? $\newline$ $27, 42, 57, 72, \dots$ $\newline$ 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

27, 42, 57, 72, \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: $27, 42, 57, 72, ext{...}$ Are the consecutive differences in the sequence equal? $\newline$ $42 - 27 = 15$ , $57 - 42 = 15$ , $72 - 57 = 15$ . $\newline$ 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. $\newline$ $\frac{42}{27}$ does not equal $\frac{57}{42}$ , and neither equals $\frac{72}{57}$ . $\newline$ Therefore, the sequence does not have a common ratio and is not a geometric sequence.
Final Conclusion: Based on the findings from the previous steps, the sequence is not geometric but is arithmetic because it has a common difference. Therefore, the correct choice is: $\newline$ (A) arithmetic.