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OAU Post-UTME Mathematics 2023 Question 3

Question 3

Progressions

If 1/2, 1/x, 1/3 are successive terms of an arithmetic progression, find the value of (2 − x)/(x − 3).

  1. A.−1/2
  2. B.2/5
  3. C.2/3
  4. D.1/4
Show the answer and explanation

Answer: C (2/3)

Explanation

In an A.P. the middle term is the average: 2/x = 1/2 + 1/3 = 5/6, so x = 12/5. Then (2 − 12/5)/(12/5 − 3) = (−2/5)/(−3/5) = 2/3.