21M.1.SL.TZ1.8

pestleMathematicsAISLPaper 121M· sl-1-2-arithmetic-sequences-and-series, sl-2-4-key-features-of-graphs-intersections-using-technologysource ↗

Charlie and Daniella each began a fitness programme. On day one, they both ran $500 m$ . On each subsequent day, Charlie ran $100 m$ more than the previous day whereas Daniella increased her distance by $2 %$ of the distance ran on the previous day.

Calculate how far

Charlie ran on day $20$ of his fitness programme.

[2]

a.i.

Daniella ran on day $20$ of her fitness programme.

[3]

a.ii.

On day $n$ of the fitness programmes Daniella runs more than Charlie for the first time.

Find the value of $n$ .

[3]

Markscheme / solution

attempt to find $u_{20}$ using an arithmetic sequence (M1)

e.g. $u_{1} = 500$ and $d = 100$ OR $u_{20} = 500 + 1900$ OR $500, 600, 700, \dots$

(Charlie ran) $2400 m$ A1

[2 marks]

a.i.

$(r =) 1.02$ (A1)

attempt to find $u_{20}$ using a geometric sequence (M1)

e.g. $u_{1} = 500$ and a value for $r$ OR $500 \times r^{19}$ OR $500, 510, 520.2, \dots$

(Daniella ran) $728 m (728.405 \dots)$ A1

[3 marks]

a.ii.

$500 \times 1 . 02^{n - 1} > 500 + (n - 1) \times 100$ (M1)

attempt to solve inequality (M1)

$n > 184.215 \dots$

$n = 185$ A1

[3 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]