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For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence). -2x-6,quad-2x-8,quad-2x-10,quad dots 2 14 -2 -14

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).\newline−2x−6,−2x−8,−2x−10,… -2 x-6, \quad-2 x-8, \quad-2 x-10, \quad \ldots \newline22\newline1414\newline−2 -2 \newline−14 -14

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Q. For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).\newline−2x−6,−2x−8,−2x−10,… -2 x-6, \quad-2 x-8, \quad-2 x-10, \quad \ldots \newline22\newline1414\newline−2 -2 \newline−14 -14
  1. Identify Sequence Type: First, let's identify if the sequence is arithmetic or geometric. An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio between consecutive terms.
  2. Check for Arithmetic Sequence: To determine if the sequence is arithmetic, we calculate the difference between the second and first term, and then the difference between the third and second term.\newlineDifference between second and first term: (−2x−8)−(−2x−6)=−2x−8+2x+6=−2(-2x - 8) - (-2x - 6) = -2x - 8 + 2x + 6 = -2\newlineDifference between third and second term: (−2x−10)−(−2x−8)=−2x−10+2x+8=−2(-2x - 10) - (-2x - 8) = -2x - 10 + 2x + 8 = -2\newlineSince the differences are the same, it is an arithmetic sequence with a common difference of −2-2.
  3. Confirm Arithmetic Sequence: We do not need to check for a common ratio because we have already determined that the sequence is arithmetic, not geometric.

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