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What kind of sequence is this?\newline1,7,49,343,…1, 7, 49, 343, \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?\newline1,7,49,343,…1, 7, 49, 343, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Identify given sequence: Identify the given sequence.\newlineThe given sequence is 1,7,49,343,…1, 7, 49, 343, \ldots
  2. Check arithmetic: Check if the sequence is arithmetic by finding the difference between consecutive terms.\newline7−1=67 - 1 = 6\newline49−7=4249 - 7 = 42\newline343−49=294343 - 49 = 294\newlineThe differences are not the same, so the sequence is not arithmetic.
  3. Check geometric: Check if the sequence is geometric by finding the ratio between consecutive terms. \newline71=7\frac{7}{1} = 7\newline497=7\frac{49}{7} = 7\newline34349=7\frac{343}{49} = 7\newlineThe ratios are the same, so the sequence is geometric.
  4. Determine sequence type: Determine the type of sequence based on the findings from steps 22 and 33. Since the sequence has a common ratio but not a common difference, it is a geometric sequence.

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