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Find the common difference of the arithmetic sequence 9,12,15,dots Answer:

Find the common difference of the arithmetic sequence 9,12,15,… 9,12,15, \ldots \newlineAnswer:

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Full solution

Q. Find the common difference of the arithmetic sequence 9,12,15,… 9,12,15, \ldots \newlineAnswer:
  1. Identify pattern: Identify the pattern in the sequence.\newlineThe given sequence is 9,12,15,…9, 12, 15, \ldots, which suggests that it is an arithmetic sequence because it appears that each term increases by a constant amount.
  2. Calculate difference: Calculate the common difference between consecutive terms.\newlineTo find the common difference, subtract the first term from the second term: 12−9=312 - 9 = 3.
  3. Verify consistency: Verify the common difference with another pair of consecutive terms.\newlineSubtract the second term from the third term to ensure the common difference is consistent: 15−12=315 - 12 = 3.
  4. Conclude common difference: Conclude the common difference of the sequence.\newlineSince both differences calculated are the same, the common difference of the arithmetic sequence is 33.

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