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Grade 12 · Number Patterns, Sequences and Series
Series, Sigma Notation & Convergence (Grade 12)
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  / 29

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    The general term of an arithmetic sequence is Tₙ = 2n + 4. Determine T₁₀.
    (1)
  2. 2
    Determine the sum of the first 19 terms of Tₙ = 2n + 4.
    (3)
  3. 3
    Evaluate ∑n=120 (3n − 1)
    (3)
  4. 4
    How many terms are there in ∑n=310 Tₙ?
    (1)
  5. 5
    Write 2 + 5 + 8 + … + 59 in sigma notation.
    (3)
  6. 6
    Determine S∞ for 8 + 4 + 2 + 1 + …
    (2)
  7. 7
    Determine the values of x for which ∑ 3(2x)n − 1 converges.
    (3)
  8. 8
    Calculate S₁₀ for the geometric series 2 + 6 + 18 + …
    (3)
  9. 9
    Derive the formula Sₙ = n/2 (a + l) for an arithmetic series.
    (4)
  10. 10
    Derive the formula for the sum of the first n terms of a geometric series.
    (4)
  11. 11
    Explain why the sum to infinity only exists when −1 < r < 1.
    (2)
TOTAL: 29 marks
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