What kind of sequence is this? 115, 95, 75, 55, ... 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: 115, 95, 75, 55, ... Are the consecutive differences in the sequence equal? 95 - 115 = -20, 75 - 95 = -20, 55 - 75 = -20. 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. 95 / 115 does not equal 75 / 95, nor does it equal 55 / 75. The ratios are not consistent, so the sequence is not geometric.Final Conclusion: Based on the previous steps, we can conclude that the sequence is arithmetic because it has a common difference, but it is not geometric because it does not have a common ratio.

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What kind of sequence is this? $\newline$ $115, 95, 75, 55, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither $\newline$

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Algebra 2

Classify formulas and sequences

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Q. What kind of sequence is this?

\newline

115, 95, 75, 55, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

\newline

Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: $115, 95, 75, 55, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $95 - 115 = -20$ , $\newline$ $75 - 95 = -20$ , $\newline$ $55 - 75 = -20$ . $\newline$ 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. $\frac{95}{115}$ does not equal $\frac{75}{95}$ , nor does it equal $\frac{55}{75}$ . The ratios are not consistent, so the sequence is not geometric.
Final Conclusion: Based on the previous steps, we can conclude that the sequence is arithmetic because it has a common difference, but it is not geometric because it does not have a common ratio.