What kind of sequence is this? 150, 138, 126, 114, ... 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: 150, 138, 126, 114, ... Are the consecutive differences in the sequence equal? Let's calculate: 138 - 150 = -12, 126 - 138 = -12, 114 - 126 = -12. The consecutive differences in the sequence are equal, each being -12.Identify Arithmetic Sequence: Since the differences between consecutive terms are constant, this indicates that the sequence is an arithmetic sequence. There is no need to check for a common ratio as in a geometric sequence because the presence of a common difference is sufficient to classify it as arithmetic.Conclusion: An arithmetic sequence is defined by having a common difference between consecutive terms. Since we have established that the sequence has a common difference of -12, we can conclude that the sequence is arithmetic.

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What kind of sequence is this? $\newline$ $150, 138, 126, 114, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Math Problems

Algebra 2

Classify formulas and sequences

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Q. What kind of sequence is this?

\newline

150, 138, 126, 114, \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: $150, 138, 126, 114, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? Let's calculate: $\newline$ $138 - 150 = -12$ , $\newline$ $126 - 138 = -12$ , $\newline$ $114 - 126 = -12$ . $\newline$ The consecutive differences in the sequence are equal, each being $-12$ .
Identify Arithmetic Sequence: Since the differences between consecutive terms are constant, this indicates that the sequence is an arithmetic sequence. There is no need to check for a common ratio as in a geometric sequence because the presence of a common difference is sufficient to classify it as arithmetic.
Conclusion: An arithmetic sequence is defined by having a common difference between consecutive terms. Since we have established that the sequence has a common difference of $-12$ , we can conclude that the sequence is arithmetic.