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Find the common difference of the arithmetic sequence -5,-1,3,dots Answer:

Find the common difference of the arithmetic sequence −5,−1,3,… -5,-1,3, \ldots \newlineAnswer:

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Full solution

Q. Find the common difference of the arithmetic sequence −5,−1,3,… -5,-1,3, \ldots \newlineAnswer:
  1. Identify Pattern: Identify the pattern in the sequence to determine if it is arithmetic.\newlineThe sequence progresses from −5-5 to −1-1, then from −1-1 to 33. This suggests a consistent increase between terms, indicating an arithmetic sequence.
  2. Calculate Common Difference: Calculate the common difference between the first two terms.\newlineThe second term −1-1 minus the first term −5-5 equals 44 (−1−(−5)=4)(-1 - (-5) = 4).
  3. Verify Difference: Verify the common difference by checking the difference between the second and third terms.\newlineThe third term 33 minus the second term −1-1 also equals 44 3−(−1)=43 - (-1) = 4.
  4. Conclude Common Difference: Conclude that the common difference is consistent across the terms checked.\newlineSince both differences calculated are the same, the common difference for the sequence is 44.

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