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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). -6x-6,quad-8x-2,quad-10 x+2,quad".. " -2x-4 -2x+4 2x-4 2x+4

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−6x−6,−8x−2,−10x+2,..  -6 x-6, \quad-8 x-2, \quad-10 x+2, \quad \text {.. } \newline−2x−4 -2 x-4 \newline−2x+4 -2 x+4 \newline2x−4 2 x-4 \newline2x+4 2 x+4

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Full solution

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−6x−6,−8x−2,−10x+2,..  -6 x-6, \quad-8 x-2, \quad-10 x+2, \quad \text {.. } \newline−2x−4 -2 x-4 \newline−2x+4 -2 x+4 \newline2x−4 2 x-4 \newline2x+4 2 x+4
  1. Determine Sequence Type: First, let's determine whether 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. We will look at the differences between consecutive terms to check for an arithmetic sequence.
  2. Calculate 11st Difference: Calculate the difference between the first and second terms: (−8x−2)−(−6x−6)=−8x−2+6x+6=−2x+4(-8x - 2) - (-6x - 6) = -8x - 2 + 6x + 6 = -2x + 4
  3. Calculate 22nd Difference: Calculate the difference between the second and third terms: \newline(−10x+2)−(−8x−2)=−10x+2+8x+2=−2x+4(-10x + 2) - (-8x - 2) = -10x + 2 + 8x + 2 = -2x + 4
  4. Confirm Arithmetic Sequence: Since the differences between consecutive terms are the same (−2x+4-2x + 4), we can conclude that the sequence is arithmetic with a common difference of −2x+4-2x + 4.

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