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Mathematics · Grades 10–12

Sum of an arithmetic sequence

Pair the first and last terms; each pair has the same total.

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The key idea

Pair the first and last terms; each pair has the same total.

Sₙ = n[2a₁ + (n − 1)d]/2

Worked examples

Find the sum of the first 18 terms of an arithmetic sequence with first term 18 and common difference 10.

18 × (2 × 18 + (18 − 1) × 10) ÷ 2 = 1854

1854

Find the sum of the first 25 terms of an arithmetic sequence with first term 3 and common difference 4.

25 × (2 × 3 + (25 − 1) × 4) ÷ 2 = 1275

1275

Try it yourself

  1. Find the sum of the first 10 terms of an arithmetic sequence with first term 22 and common difference 10.

  2. Find the sum of the first 16 terms of an arithmetic sequence with first term 25 and common difference 2.

Check your understanding

Answers and marking notes
  1. 670

    10 × (2 × 22 + (10 − 1) × 10) ÷ 2 = 670

  2. 640

    16 × (2 × 25 + (16 − 1) × 2) ÷ 2 = 640

Further reading and review references

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Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.