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Marie sent 1212 pieces of mail in October, 4848 pieces of mail in November, 192192 pieces of mail in December, and 768768 pieces of mail in January. What kind of sequence is this?\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

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Q. Marie sent 1212 pieces of mail in October, 4848 pieces of mail in November, 192192 pieces of mail in December, and 768768 pieces of mail in January. What kind of sequence is this?\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. List Mail Sent: List the number of pieces of mail sent by Marie in each month.\newlineOctober: 1212\newlineNovember: 4848\newlineDecember: 192192\newlineJanuary: 768768\newlineSequence: 12,48,192,76812, 48, 192, 768
  2. Check Arithmetic: Determine if the sequence is arithmetic by checking if the differences between consecutive terms are equal.\newlineDifference between November and October: 4812=3648 - 12 = 36\newlineDifference between December and November: 19248=144192 - 48 = 144\newlineDifference between January and December: 768192=576768 - 192 = 576\newlineCheck if the differences are equal: 3614457636 \neq 144 \neq 576\newlineThe differences are not equal, so the sequence is not arithmetic.
  3. Check Geometric: Determine if the sequence is geometric by checking if the ratios between consecutive terms are equal.\newlineRatio of November to October: 4812=4\frac{48}{12} = 4\newlineRatio of December to November: 19248=4\frac{192}{48} = 4\newlineRatio of January to December: 768192=4\frac{768}{192} = 4\newlineCheck if the ratios are equal: 4=4=44 = 4 = 4\newlineThe ratios are equal, so the sequence is geometric.

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