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

The sum to infinity of a GP is 40 and its first term is 10. What is the sum of the first three terms of this GP?

The ratio is three-quarters because 40 equals 10 divided by (1 minus r). The first three terms are 10, 7.5 and 5.625, which total 23.125.

  1. A16.25
  2. B23.75
  3. C28.75
  4. D33.75Correct

Explanation

40 = 10/(1 - r) gives 1 - r = 1/4, so r = 3/4. The terms are 10, 7.5, 5.625, whose sum is 23.125. Check with formula: 10(1 - 27/64)/(1/4) = 40 x 37/64 = 23.125. None of the listed values equals this, so the key is incorrectly listed.

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