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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Arithmetic Progression and Geometric Progression

The production of a unit in Coimbatore doubles every year, starting at 3,000 units in the first year. In which year will the production first exceed 40,000 units?

Production first exceeds 40,000 units in the fifth year. Output in year n is 3,000 times 2 to the power n minus 1. Year 4 gives 24,000 units, which is below the target, while year 5 gives 48,000 units, which is above it.

  1. AFourth year
  2. BSeventh year
  3. CFifth year
  4. DSixth yearCorrect

Explanation

The nth year output is 3000 x 2^(n-1). Year 4 gives 24,000, year 5 gives 48,000, so the first year above 40,000 is year 5. Check the options: the fifth year is therefore correct.

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