What kind of sequence is this? 181, 161, 141, 121, ... 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: 181, 161, 141, 121, ... Are the consecutive differences in the sequence equal? 161 - 181 = -20, 141 - 161 = -20, 121 - 141 = -20. The consecutive differences in the sequence are equal and the common difference is -20.Check for Common Ratio: Since the sequence has a common difference, it could be an arithmetic sequence. Let's check if it could also be a geometric sequence by finding the ratios between consecutive terms. Are the ratios between consecutive terms in the sequence equal? 161 / 181 ≠ 141 / 161 ≠ 121 / 141. The ratios are not equal, so the sequence is not geometric.Identify Sequence Type: Arithmetic sequence: Consecutive terms have a common difference. Geometric sequence: Consecutive terms have a common ratio. 181, 161, 141, 121, ... What type of sequence is this? The sequence has a common difference (-20) and does not have a common ratio. Therefore, it is an arithmetic sequence.

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What kind of sequence is this? $\newline$ $181, 161, 141, 121, \dots$ $\newline$ 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

181, 161, 141, 121, \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: $181, 161, 141, 121, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $161 - 181 = -20$ , $\newline$ $141 - 161 = -20$ , $\newline$ $121 - 141 = -20$ . $\newline$ The consecutive differences in the sequence are equal and the common difference is $-20$ .
Check for Common Ratio: Since the sequence has a common difference, it could be an arithmetic sequence. Let's check if it could also be a geometric sequence by finding the ratios between consecutive terms. $\newline$ Are the ratios between consecutive terms in the sequence equal? $\newline$ $\frac{161}{181} \neq \frac{141}{161} \neq \frac{121}{141}$ . $\newline$ The ratios are not equal, so the sequence is not geometric.
Identify Sequence Type: Arithmetic sequence: Consecutive terms have a common difference. Geometric sequence: Consecutive terms have a common ratio. $181, 161, 141, 121, \ldots$ What type of sequence is this? The sequence has a common difference ( $-20$ ) and does not have a common ratio. Therefore, it is an arithmetic sequence.