Unit 1: Number and Algebra
Topic 1.3: Geometric Sequences and Series Questions
Practice 20 exam-style questions for IB Math AA SL Topic 1.3. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Show that2 marks
2024
Consider the geometric sequence a, s, t, …, where a, s, t ≠ 0.
Show that t/a = (s/a)2.
Show that t/a = (s/a)2.
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2024
A geometric sequence has first term 2 and third term 18, and its second term is negative.
Write down the first four terms of the sequence.
Write down the first four terms of the sequence.
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2021
At the start of hour 1 a culture holds 800 bacteria, and the number triples every hour.
Write down an expression, in terms of n, for the number of bacteria at the start of hour n.
Write down an expression, in terms of n, for the number of bacteria at the start of hour n.
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2024
Consider the geometric sequence a, s, t, w, …, where a, s, t, w ≠ 0.
Show that st = aw.
Show that st = aw.
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2025
A geometric sequence begins −2, 2, −2, …
Write down the sum of the first 2m − 1 terms, where m ∈ ℤ+.
Write down the sum of the first 2m − 1 terms, where m ∈ ℤ+.
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2023
A geometric sequence has common ratio r = ±3 and u2 = −4. It is given that u7 > 0.
Find u3.
Find u3.
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2026
Write down an expression for .
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2024
Consider the geometric sequence , where .
Show that .
Show that .
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2022
Consider the series log2 y + log2 yp + log2 y9 + …, where y > 1, and p ≠ 0. The series is geometric.
Show that p = ±3.
Show that p = ±3.
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2025
Consider a sequence whose first three terms are u1 = k − 2, u2 = −2k − 2 and u3 = 3k + 5, where k ∈ ℤ.
Given that the sequence is geometric, show that k2 + 9k + 14 = 0.
Given that the sequence is geometric, show that k2 + 9k + 14 = 0.
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2026
A geometric sequence a1, a2, a3, … has common ratio r. A second sequence b1, b2, b3, … is defined by bn = (an)3 and has common ratio q.
Show that q = r3.
Show that q = r3.
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2025
The terms of a geometric sequence are 4, −4, 4, −4, …
Write down S20, the sum of the first 20 terms.
Write down S20, the sum of the first 20 terms.
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2025
Cube C1 has edge 2 cm. Each later cube has edge twice as long as the one before.
Show that the volume of Cn is 8n cm3.
Show that the volume of Cn is 8n cm3.
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2023
A geometric sequence has common ratio r = ±√2 and 4th term 8. It is given that u11 > 0.
Find u5.
Find u5.
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2026
A geometric sequence has first term 4 and common ratio 3. Find the 6th term.
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2026
Interpret the value in the context of the model.
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2024
A model gives with .
Verify that .
Verify that .
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2022
Consider the series ln x + ln xp + ln x1/4 + …, where x > 1, and p ≠ 0. The series is geometric.
Show that p = ±1/2.
Show that p = ±1/2.
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2021
The first echo of a shout has intensity 80 units. Each later echo has 0.6 of the intensity of the one before.
Write down an expression, in terms of n, for the intensity of the nth echo.
Write down an expression, in terms of n, for the intensity of the nth echo.
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