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What kind of sequence is this?\newline181,161,141,121,…181, 161, 141, 121, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

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Q. What kind of sequence is this?\newline181,161,141,121,…181, 161, 141, 121, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: 181,161,141,121,…181, 161, 141, 121, \ldots\newlineAre the consecutive differences in the sequence equal? \newline161−181=−20161 - 181 = -20, \newline141−161=−20141 - 161 = -20, \newline121−141=−20121 - 141 = -20. \newlineThe consecutive differences in the sequence are equal and the common difference is −20-20.
  2. 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.\newlineAre the ratios between consecutive terms in the sequence equal? \newline161181≠141161≠121141\frac{161}{181} \neq \frac{141}{161} \neq \frac{121}{141}. \newlineThe ratios are not equal, so the sequence is not geometric.
  3. Identify Sequence Type: Arithmetic sequence: Consecutive terms have a common difference. Geometric sequence: Consecutive terms have a common ratio. 181,161,141,121,…181, 161, 141, 121, \ldots What type of sequence is this? The sequence has a common difference (−20-20) and does not have a common ratio. Therefore, it is an arithmetic sequence.

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