IB Maths AI SL 1.3 Geometric sequences and series Question Bank

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

Find a common ratio and use SL nth-term or finite-sum formulae with correct indices.
Model repeated growth or decay and interpret the sum or term in the stated context.
Check ratio, domain, rounding and units when reporting a geometric-sequence result.

[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 $177.587 \ldots$

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SL 1.3—Geometric sequences and series question 1

Question (a)

Question (b)