IB Maths AI HL 1.3 Geometric sequences and series Question Bank

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

Exam points

Solve HL geometric-series problems involving parameters, convergence conditions and multi-stage growth or decay.
Use logarithms or inequalities to justify a term threshold and explain what the model predicts.
Compare equivalent ratio forms and validate exact or rounded answers against the context.

[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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SL 1.3—Geometric sequences and series question 1

Question (a)

Question (i)

Question (ii)