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While organizing her DVD collection, Savannah put 22 DVDs on the first rack, 1414 DVDs on the second rack, 9898 DVDs on the third rack, and 686686 DVDs on the fourth rack. What kind of sequence is this?\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

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Q. While organizing her DVD collection, Savannah put 22 DVDs on the first rack, 1414 DVDs on the second rack, 9898 DVDs on the third rack, and 686686 DVDs on the fourth rack. What kind of sequence is this?\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Identify Sequence Type: To determine the type of sequence, we need to look at the pattern of numbers and see if there is a common difference (which would indicate an arithmetic sequence) or a common ratio (which would indicate a geometric sequence). Let's examine the given numbers: 2,14,98,6862, 14, 98, 686.
  2. Check for Common Difference: First, let's check for a common difference by subtracting each term from the subsequent term: \newline142=1214 - 2 = 12\newline9814=8498 - 14 = 84\newline68698=588686 - 98 = 588\newlineThe differences are not constant, so this is not an arithmetic sequence.
  3. Check for Common Ratio: Next, let's check for a common ratio by dividing each term by the previous term:\newline14÷2=714 \div 2 = 7\newline98÷14=798 \div 14 = 7\newline686÷98=7686 \div 98 = 7\newlineThe ratio is constant, so this is a geometric sequence.

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