A start-up company tracks its daily net cash flow, CnC_nCn, in pounds (£\pounds£). The cash flow follows an arithmetic sequence with first term aaa and common difference ddd.
The total net cash flow over the first 12 days is £\pounds£ 432.
Show that 4a+22d=1444a + 22d = 1444a+22d=144.
Given that the total net cash flow over the first 30 days is £\pounds£ 0, determine the total net cash flow over the first 15 days.
SnS_nSn represents the sum of the daily net cash flow for the first nnn days. Explain why the value you calculated in part (b) is the maximum value of SnS_nSn.
308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.