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Elizabeth sent 88 e-mails on Tuesday, 4040 e-mails on Wednesday, 200200 e-mails on Thursday, and 1,0001,000 e-mails on Friday. What kind of sequence is this?\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. Elizabeth sent 88 e-mails on Tuesday, 4040 e-mails on Wednesday, 200200 e-mails on Thursday, and 1,0001,000 e-mails on Friday. What kind of sequence is this?\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Examine Pattern of Numbers: To determine the type of sequence, we need to examine the pattern of numbers. An arithmetic sequence has a common difference between terms, while a geometric sequence has a common ratio. Let's check for a common difference first.\newlineWe calculate the differences between consecutive terms:\newlineDifference between Wednesday and Tuesday: 40−8=3240 - 8 = 32\newlineDifference between Thursday and Wednesday: 200−40=160200 - 40 = 160\newlineDifference between Friday and Thursday: 1,000−200=8001,000 - 200 = 800
  2. Calculate Differences: Now let's check if the differences form a pattern that indicates an arithmetic sequence. If the differences are not constant, it is not an arithmetic sequence.\newlineComparing the differences:\newline3232 (from Tuesday to Wednesday) is not equal to 160160 (from Wednesday to Thursday), which is not equal to 800800 (from Thursday to Friday).\newlineSince the differences are not constant, this is not an arithmetic sequence.
  3. Check for Arithmetic Sequence: Next, we check for a common ratio to determine if it's a geometric sequence. We calculate the ratios between consecutive terms:\newlineRatio between Wednesday and Tuesday: 408=5\frac{40}{8} = 5\newlineRatio between Thursday and Wednesday: 20040=5\frac{200}{40} = 5\newlineRatio between Friday and Thursday: 1,000200=5\frac{1,000}{200} = 5
  4. Calculate Ratios: Now let's check if the ratios are constant, which would indicate a geometric sequence.\newlineComparing the ratios:\newline55 (from Tuesday to Wednesday) is equal to 55 (from Wednesday to Thursday), which is equal to 55 (from Thursday to Friday).\newlineSince the ratios are constant, this is a geometric sequence.

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