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Find the common difference of the arithmetic sequence 12,9,6,dots Answer:

Find the common difference of the arithmetic sequence 12,9,6,… 12,9,6, \ldots \newlineAnswer:

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Full solution

Q. Find the common difference of the arithmetic sequence 12,9,6,… 12,9,6, \ldots \newlineAnswer:
  1. Identify Pattern: Identify the pattern in the sequence to determine if it is arithmetic. The sequence shows a consistent decrease from one term to the next, which suggests it is an arithmetic sequence.
  2. Calculate Common Difference: Calculate the common difference between consecutive terms.\newlineThe difference between the first term 1212 and the second term 99 is 12−9=312 - 9 = 3.\newlineSimilarly, the difference between the second term 99 and the third term 66 is 9−6=39 - 6 = 3.
  3. Verify Consistency: Verify that the common difference is consistent throughout the sequence.\newlineSince both differences calculated are the same 33, the common difference is consistent.

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