SPM.1.SL.TZ0.2

pestleMathematicsAISLPaper 1SPM· sl-1-2-arithmetic-sequences-and-seriessource ↗

The Osaka Tigers basketball team play in a multilevel stadium.

The most expensive tickets are in the first row. The ticket price, in Yen (¥), for each row forms an arithmetic sequence. Prices for the first three rows are shown in the following table.

Write down the value of the common difference, $d$

[1]

Calculate the price of a ticket in the 16th row.

[2]

Find the total cost of buying 2 tickets in each of the first 16 rows.

[3]

Markscheme / solution

( $d$ =) − 250 A1

[1 mark]

$\left( {{u_{16}} = } \right)6800 + \left( {16 - 1} \right)\left( { - 250} \right)$ M1

(¥)3050 A1

[2 marks]

$\left( {{S_{16}} = } \right)\left( {\frac{{16}}{2}} \right)\left( {2 \times 6800 + \left( {16 - 1} \right)\left( { - \,250} \right)} \right) \times 2$ M1M1

Note: Award M1 for correct substitution into arithmetic series formula.
Award M1 for multiplication by 2 seen.

$\left( {{S_{16}} = } \right)\left( {\frac{{16}}{2}} \right)\left( {6800 + 3050} \right) \times 2$ M1M1

Note: Award M1 for correct substitution into arithmetic series formula.
Award M1 for multiplication by 2 seen.

(¥)158 000 (157 600) A1

[3 marks]

Examiners’ report

[N/A]