IB Maths AI SL 1.3 Geometric Sequences and Series Questions

Practise IB Maths AI SL 1.3 through questions on common ratios, nth terms, finite sums and repeated growth or decay in practical contexts

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.

Learn this topic

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

[Maximum number: 7]

A marathon is a race over a distance of 42.19 km .

(a)

Find the first week during which Davi runs more than 42 km .

[ 4 ]

(d) METHOD 1
$3(1.2)^{n-1}$

Note: Award (A1) for correct substitution into geometric sequence formula.
comparing their geometric expression to 42
e.g. $3(1.2)^{n-1}>42$ OR $3(1.2)^{n-1}=42$ $(n=) 15.4747 \ldots$ seen OR $38.5175 \ldots$ and $46.2210 \ldots$ seen (from table)

16 (weeks)

METHOD 2

List of values see. At least 3, 3.6, 4.32 etc
$38.5175 \ldots$ and $46.2210 \ldots$ seen

16 (weeks)

(b)

Find the first week that the total distance that Davi has run, since the start of training, exceeds 150 km .

[ 3 ]

METHOD 1 attempt to substitute into geometric series formula

Note: FT their r from (d).

150<\frac{3\left(1-1.2^{n}\right)}{1-1.2} \text { OR } 150=\frac{3\left(1-1.2^{n}\right)}{1-1.2} \text { OR } 13.1520 \ldots

14 (weeks)

METHOD 2
evidence using tables in GDC or adding the first 14 terms both crossover values seen, e.g $145.589 \ldots$ and $177.587 \ldots$

All question bank results loaded

Learn this topic

IB Maths AI SL 1.3 Geometric Sequences and Series Questions question 1

Question (a)

Question (b)