Unit 1: Number and Algebra
Topic 1.11: Infinite geometric series (HL only) Questions
Practice 11 exam-style questions for IB Math AI SL Topic 1.11. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
The sum to infinity formula S∞ = u₁/(1 − r) may be used only when:
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2026
A geometric series has u₁ = 9 and r = 1/3. Its sum to infinity is:
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A geometric series has first term 20 and common ratio 0.8. Find the sum to infinity.
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For which value of r does the series NOT have a sum to infinity?
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A pendulum swings through an arc of 90 cm on its first swing. Each swing covers 75% of the previous swing's arc. Find the total distance the pendulum tip travels before stopping.
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A convergent series has S∞ = 50 and u₁ = 10. The common ratio is:
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A patient takes an 8 mg dose of a drug each day. By the next dose, 25% of the amount present remains. Find the long-run steady amount in the body just after a dose, and interpret it.
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A convergent geometric series has first term 15 and sum to infinity 45. Find the common ratio.
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A ball dropped from 4 m rebounds to 50% of its height each bounce. The total distance it travels is found from:
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2026
A newly planted tree grows 1.5 m in its first year. Each following year it grows 80% of the previous year's growth.
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2026
Determine the values of x for which the geometric series 1 + 2x + 4x² + 8x³ + … has a sum to infinity, and find that sum when x = 0.3.
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