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What kind of sequence is this?\newline4,24,144,864,…4, 24, 144, 864, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

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Identify arithmetic and geometric sequencesright chevron icon

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Q. What kind of sequence is this?\newline4,24,144,864,…4, 24, 144, 864, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Identify Given Sequence: Identify the given sequence and list the terms.\newlineThe given sequence is 44, 2424, 144144, 864864, ...
  2. Check Arithmetic Differences: Determine if the sequence is arithmetic by checking if the differences between consecutive terms are equal.\newlineCalculate the difference between the second and the first term: 24−4=2024 - 4 = 20\newlineCalculate the difference between the third and the second term: 144−24=120144 - 24 = 120\newlineSince 2020 is not equal to 120120, the differences are not equal.\newlineThe sequence is not arithmetic.
  3. Check Geometric Ratios: Determine if the sequence is geometric by checking if the ratios between consecutive terms are equal.\newlineCalculate the ratio of the second term to the first term: 244=6\frac{24}{4} = 6\newlineCalculate the ratio of the third term to the second term: 14424=6\frac{144}{24} = 6\newlineCalculate the ratio of the fourth term to the third term: 864144=6\frac{864}{144} = 6\newlineSince all ratios are equal to 66, the sequence is geometric.

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