IB Maths AI SL 1.2 Arithmetic Sequences and Series Questions

Practise IB Maths AI SL 1.2 through questions on arithmetic terms, common differences, finite sums and applied models such as fees, savings and repeated change.

Exam points

Use the nth-term formula to model an arithmetic sequence from its first term and common difference, then determine a specified term or unknown parameter.
Use finite arithmetic-series sums, sigma notation or equivalent expressions to calculate totals, averages and cumulative quantities.
Translate applied repeated-change contexts into an arithmetic model and solve thresholds, index restrictions or resource limits.
Interpret and check the result using the correct index, units, rounding and real-world meaning.

[Maximum number: 5]

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

(a)

Find the week during which Rolando runs 42 km .

[ 3 ]

METHOD 1 attempt to substitute into arithmetic sequence formula
$42=6+(n-1) \times 2$ OR 42=2 n+4
( n= ) 19

METHOD 2
list of any consecutive terms ending on/above 42
at least two correct terms (not including 6, 8 and 10)
( n= ) 19

(b)

Find the total distance that Rolando runs in the first 10 weeks.

Davi runs 3 km in the first week. In each subsequent week he runs 20 % further than the previous week. These distances form the terms of a geometric sequence.

[ 2 ]

METHOD 1
$\left(S_{10}=\right) \frac{10}{2}(2 \times 6+(10-1) 2)$ $150(\mathrm{~km})$

METHOD 2
summing (some) correct terms up to 24 OR list of correct cumulative values $6+8+10+\ldots+24$ OR $6,14,24,36 \ldots$ $150(\mathrm{~km})$

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IB Maths AI SL 1.2 Arithmetic Sequences and Series Questions question 1

Question (a)

Question (b)