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

The sum of the first n terms of a sequence is given by Sn = 3n² + 2n. What is the 10th term of the sequence, and what kind of progression does it form?

The 10th term is 59 and the sequence is an arithmetic progression with common difference 6. Subtracting S9, which is 261, from S10, which is 320, gives 59. In general the nth term is 6n - 1, so consecutive terms differ by a constant 6.

  1. ATerm is 59; arithmetic progression with common difference 6Correct
  2. BTerm is 320; geometric progression with ratio 3
  3. CTerm is 59; geometric progression
  4. DTerm is 65; arithmetic progression with common difference 6

Explanation

The 10th term = S10 - S9 = (300 + 20) - (243 + 18) = 320 - 261 = 59. In general Tn = Sn - Sn-1 = 6n - 1, so the difference between consecutive terms is 6, a constant, and the sequence is an AP. Check: T10 = 60 - 1 = 59. Option 65 wrongly uses 6n + 5.

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