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

Three numbers are in GP with a product of 216 and a sum of 21. If the common ratio is greater than 1, what is the largest number?

The largest number is 12. Writing the numbers as a/r, a and ar, the product gives a = 6. The sum condition leads to 2r squared minus 5r plus 2 = 0, so r = 2 for r above 1. The numbers are 3, 6 and 12, with product 216 and sum 21.

  1. A12Correct
  2. B18
  3. C9
  4. D6

Explanation

Let the numbers be a/r, a, ar. Product a^3 = 216, so a = 6. Sum: 6/r + 6 + 6r = 21, so 6r + 6/r = 15, giving 2r^2 - 5r + 2 = 0, so r = 2 or 1/2. With r = 2 the numbers are 3, 6, 12. Check: product 216, sum 21. The largest is 12.

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