Kenneth ChengMathematical modeling
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An arithmetic sequence has partial sum Sₙ=n². Find its tenth term.

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TOPIC 01

2021 JM01

S₁₀ is a sum of ten terms, not the tenth term itself.

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Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

An arithmetic sequence has partial sum Sₙ=n². Find its tenth term.

Sn=n2S_n=n^2

Official paper · jm01-2021 · I.3 · PDF 2

Official original and suggested answers ↗ · Suggested answer PDF page 5

Skills and prerequisite lessons
  1. Option A1919
  2. Option B2121
  3. Option C2828
  4. Option D3131
  5. Option E4040

Working and explanation

BUILD THE REASONING

Hint 1
A term is the difference of consecutive partial sums.
Hint 2
Subtract S₉ from S₁₀.
Worked solution

  1. Recover the general term.

    an=Sn−Sn−1=n2−(n−1)2=2n−1a_n=S_n-S_{n-1}=n^2-(n-1)^2=2n-1

  2. Evaluate at n=10.

    a10=20−1=19a_{10}=20-1=19

A: 19.

Checks and common pitfalls: S₁₀ is a sum of ten terms, not the tenth term itself.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • Recover the general term.
    an=Sn−Sn−1=n2−(n−1)2=2n−1a_n=S_n-S_{n-1}=n^2-(n-1)^2=2n-1
  • Evaluate at n=10.
    a10=20−1=19a_{10}=20-1=19

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