The concentration of a specific catalyst, CnC_nCn mmol/L, in a chemical reactor is recorded every hour. The process is modeled by the recurrence relation
Cn+1=15−Cn,n≥1 C_{n+1} = 15 - C_n, \quad n \ge 1 Cn+1=15−Cn,n≥1where the initial concentration is C1=4.5C_1 = 4.5C1=4.5.
Find the value of (i) C2C_2C2 (ii) C85C_{85}C85
Determine the value of ∑n=1100(4Cn−5)\sum_{n=1}^{100} (4C_n - 5)∑n=1100(4Cn−5).
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.