CMA Foundation · Fundamentals of Business Mathematics and Statistics · Arithmetic Progression and Geometric Progression
Find the sum to infinity of the series 18 + 6 + 2 + 2/3 + ...
The sum to infinity is 27. The series is a GP with first term 18 and ratio one-third, so the sum is 18 divided by (1 minus one-third), which is 18 divided by two-thirds, giving 27.
- A24
- B27Correct
- C36
- D54
Explanation
The ratio is 6/18 = 1/3, which is less than 1 in modulus. Sum = a/(1 - r) = 18/(2/3) = 27. Using 18/(1/3) = 54 is the mistake of using r instead of 1 - r.
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