IB Maths AI HL Sl 1 3 Geometric Sequences and Series Questions

Practise IB Maths AI HL 1.3 through questions that extend geometric sequences to parameters, convergence, logarithmic thresholds and applied models.

Exam points

Use the nth-term formula to determine terms, common ratios or unknown parameters of a geometric sequence.
Use finite geometric-series sums and convergence conditions to calculate totals, limiting values or accumulated quantities.
Model repeated growth, decay or alternating change and solve thresholds, time indices and multi-stage applications.
Interpret whether a geometric model is appropriate and check ratio, domain, rounding, units and contextual meaning.

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Study SL 1.3—Geometric sequences and series conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 2]

Nanthana is completing an exploration on multiplication using complex numbers. She considers a geometric sequence where $u_{1}=9$ and $r=\frac{2}{3}+\frac{2}{3} \mathrm{i}$ .

(a)

Write down the value of

[ 2 ]

(i)

$\quad u_{2}$ .

[ 1 ]

$\left(u_{2}=\right) 6+6 \mathrm{i} \quad \boldsymbol{A} \mathbf{1}$

(ii)

$u_{3}$ .

Nanthana claims that the sequence $\left|u_{1}\right|,\left|u_{2}\right|,\left|u_{3}\right|, \ldots$ also forms a geometric sequence.

[ 1 ]

$\quad\left(u_{3}=\right) 8 \mathrm{i} \quad \boldsymbol{A} \mathbf{1}$

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IB Maths AI HL Sl 1 3 Geometric Sequences and Series Questions question 1

Question (a)

Question (i)

Question (ii)