CMA Foundation · Fundamentals of Business Mathematics and Statistics · Arithmetic Progression and Geometric Progression
Three positive numbers are in GP with product 216 and the sum of the first and third numbers is 20. Which could be the geometric mean of the first and third numbers, and what is it?
The geometric mean of the first and third numbers is 6. In a three-term GP the middle term equals the geometric mean of the outer terms. The product of the three terms is the cube of the middle term, so 216 gives 6. The ends 2 and 18 sum to 20.
- A6Correct
- B10
- C12
- D36
Explanation
Let the numbers be a/r, a, ar. Product = a³ = 216, so a = 6, the middle term. The middle term of a GP is the GM of its neighbours, so GM of first and third is 6. Check: terms 2, 6, 18 sum of ends 20. The value 10 is their AM.
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