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What kind of sequence is this?\newline1,8,64,512,…1, 8, 64, 512, \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?\newline1,8,64,512,…1, 8, 64, 512, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Determine Sequence Type: To determine the type of sequence, we need to examine the relationship between consecutive terms.
  2. Check Arithmetic Sequence: First, let's check if it's an arithmetic sequence by finding the difference between consecutive terms.\newline8−1=78 - 1 = 7\newline64−8=5664 - 8 = 56\newline512−64=448512 - 64 = 448\newlineThe differences are not constant, so it is not an arithmetic sequence.
  3. Check Geometric Sequence: Now, let's check if it's a geometric sequence by finding the ratio between consecutive terms.\newline8÷1=88 \div 1 = 8\newline64÷8=864 \div 8 = 8\newline512÷64=8512 \div 64 = 8\newlineThe ratio is constant, so it is a geometric sequence.

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