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

How many terms of the arithmetic series 5 + 9 + 13 + ... must be added to get a sum of 275?

Eleven terms are needed. With first term 5 and common difference 4, the sum of n terms equals n(2n+3). Setting this equal to 275 gives 2n² + 3n - 275 = 0, whose positive root is 11. The 11 terms total 275.

  1. A10
  2. B12
  3. C11Correct
  4. D9

Explanation

Here a = 5 and d = 4. Sum = n/2 [10 + 4(n-1)] = n(2n + 3) = 275, so 2n² + 3n - 275 = 0. Factorising gives (2n + 25)(n - 11) = 0, so n = 11. Check: the 11th term is 45 and sum = 11×(5+45)/2 = 275. Taking n = 10 gives only 230.

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