- In an arithmetic series, the first term is \(a\) and the common difference is \(d\).
Show that
$$S _ { n } = \frac { n } { 2 } [ 2 a + ( n - 1 ) d ]$$
(ii) James saves money over a number of weeks to buy a printer that costs \(\pounds 64\)
He saves \(\pounds 10\) in week \(1 , \pounds 9.20\) in week \(2 , \pounds 8.40\) in week 3 and so on, so that the weekly amounts he saves form an arithmetic sequence.
Given that James takes \(n\) weeks to save exactly \(\pounds 64\)
- show that
$$n ^ { 2 } - 26 n + 160 = 0$$
- Solve the equation
$$n ^ { 2 } - 26 n + 160 = 0$$
- Hence state the number of weeks James takes to save enough money to buy the printer, giving a brief reason for your answer.