What kind of sequence is this? 167, 151, 135, 119, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Identify Sequence Type: To determine the type of sequence, we need to look at the pattern of the differences or ratios between the terms. First, let's find the difference between the consecutive terms. Difference between the first and second term: 151 - 167 = -16Find Consecutive Term Differences: Now, let's check the difference between the second and third term: 135 - 151 = -16Check for Constant Difference: Next, we check the difference between the third and fourth term: 119 - 135 = -16Confirm Arithmetic Sequence: Since the difference between each pair of consecutive terms is the same (-16), this indicates that the sequence is an arithmetic sequence.Define Arithmetic Sequence: An arithmetic sequence is defined by a constant difference between its terms. Since we have a constant difference of -16, we can conclude that the sequence is arithmetic.Conclusion: Therefore, the correct choice is (A) arithmetic.

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What kind of sequence is this? $\newline$ $167, 151, 135, 119, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Precalculus

Identify arithmetic and geometric series

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Q. What kind of sequence is this?

\newline

167, 151, 135, 119, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Identify Sequence Type: To determine the type of sequence, we need to look at the pattern of the differences or ratios between the terms. $\newline$ First, let's find the difference between the consecutive terms. $\newline$ Difference between the first and second term: $151 - 167 = -16$
Find Consecutive Term Differences: Now, let's check the difference between the second and third term: $135 - 151 = -16$
Check for Constant Difference: Next, we check the difference between the third and fourth term: $119 - 135 = -16$
Confirm Arithmetic Sequence: Since the difference between each pair of consecutive terms is the same ( $-16$ ), this indicates that the sequence is an arithmetic sequence.
Define Arithmetic Sequence: An arithmetic sequence is defined by a constant difference between its terms. Since we have a constant difference of $-16$ , we can conclude that the sequence is arithmetic.
Conclusion: Therefore, the correct choice is (A) arithmetic.