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Mathematics · Grades 10–12

Finite geometric sums

Use n terms, starting with the first term a.

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The key idea

Use n terms, starting with the first term a.

Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1

Worked examples

Find the sum of the first 4 terms of a geometric sequence with first term 4 and ratio 4.

4 × (4^4 − 1) ÷ (4 − 1) = 340

340

Find the sum of the first 4 terms of a geometric sequence with first term 12 and ratio 3.

12 × (3^4 − 1) ÷ (3 − 1) = 480

480

Try it yourself

  1. Find the sum of the first 5 terms of a geometric sequence with first term 1 and ratio 5.

  2. Find the sum of the first 3 terms of a geometric sequence with first term 4 and ratio 2.

Check your understanding

Answers and marking notes
  1. 781

    1 × (5^5 − 1) ÷ (5 − 1) = 781

  2. 28

    4 × (2^3 − 1) ÷ (2 − 1) = 28

Further reading and review references

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