What kind of sequence is this? 156, 144, 132, 120, ... 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: 156, 144, 132, 120, ... Are the consecutive differences in the sequence equal? 144 - 156 = -12, 132 - 144 = -12, 120 - 132 = -12. The consecutive differences in the sequence are equal and the common difference is -12.Identify Arithmetic Sequence: Since the sequence has a common difference, it is an arithmetic sequence. Now, let's check if it could also be a geometric sequence by finding the ratios between consecutive terms. 144 / 156 = 0.923076923..., 132 / 144 = 0.916666666..., 120 / 132 = 0.909090909... The ratios between consecutive terms are not equal.Check Geometric Sequence: An arithmetic sequence has a common difference between consecutive terms, while a geometric sequence has a common ratio between consecutive terms. Since the given 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? $\newline$ $156, 144, 132, 120, \dots$ $\newline$ 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

156, 144, 132, 120, \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: $156, 144, 132, 120, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $144 - 156 = -12$ , $132 - 144 = -12$ , $120 - 132 = -12$ . $\newline$ The consecutive differences in the sequence are equal and the common difference is $-12$ .
Identify Arithmetic Sequence: Since the sequence has a common difference, it is an arithmetic sequence. $\newline$ Now, let's check if it could also be a geometric sequence by finding the ratios between consecutive terms. $\newline$ $\frac{144}{156} = 0.923076923\ldots$ , $\frac{132}{144} = 0.916666666\ldots$ , $\frac{120}{132} = 0.909090909\ldots$ $\newline$ The ratios between consecutive terms are not equal.
Check Geometric Sequence: An arithmetic sequence has a common difference between consecutive terms, while a geometric sequence has a common ratio between consecutive terms. $\newline$ Since the given sequence has a common difference but not a common ratio, it is an arithmetic sequence and not a geometric sequence.