18M.2.SL.TZ2.T_4

pestleMathematicsAASLPaper 218M· sl-1-2-arithmetic-sequences-and-seriessource ↗

A new café opened and during the first week their profit was $60.

The café’s profit increases by $10 every week.

A new tea-shop opened at the same time as the café. During the first week their profit was also $60.

The tea-shop’s profit increases by 10 % every week.

Calculate the café’s total profit for the first 12 weeks.

[3]

Calculate the tea-shop’s total profit for the first 12 weeks.

[3]

Markscheme / solution

$\frac{{12}}{2}\left( {2 \times 60 + 11 \times 10} \right)$ (M1)(A1)(ft)

Note: Award (M1) for substituting the arithmetic series formula, (A1)(ft) for correct substitution. Follow through from their first term and common difference in part (a).

= ($) 1380 (A1)(ft)(G2)

[3 marks]

$\frac{{60\left( {{{1.1}^{12}} - 1} \right)}}{{1.1 - 1}}$ (M1)(A1)(ft)

Note: Award (M1) for substituting the geometric series formula, (A1)(ft) for correct substitution. Follow through from part (c) for their first term and common ratio.

= ($)1280 (1283.05…) (A1)(ft)(G2)

[3 marks]

Examiners’ report

[N/A]