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 OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.