Multiple choice

If 2x, 5 and 6 - x are the first three terms of the sequence, find the common difference.

  1. -4

  2. -3

  3. -1

  4. 0
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B Correct answer
Explanation

In an AP, the common difference d = second term - first term = third term - second term. 5 - 2x = (6 - x) - 5. 5 - 2x = 1 - x. 4 = x. The terms are 8, 5, 2. The common difference is 5 - 8 = -3.

AI explanation

In an arithmetic progression, the difference between consecutive terms must be constant, so 2x minus 5 equals 5 minus (6 - x). Solving the equation 2x - 5 = x - 1 gives x = 4. Substituting 4 into the terms gives the first term as 8 and the second as 5, making the common difference -3.

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