An industrial kiln's control system modulates the internal temperature, TnT_nTn in degrees Celsius, at discrete time steps nnn. The temperature sequence T1,T2,T3,…T_1, T_2, T_3, \dotsT1,T2,T3,… is defined by
Tn+1=1800−Tn T_{n+1} = 1800 - T_n Tn+1=1800−Tnwhere T1=850T_1 = 850T1=850 is the initial temperature reading.
Find the value of
(i) T2T_2T2
(ii) T121T_{121}T121
∑n=140(0.1Tn+5)\sum_{n=1}^{40} (0.1T_n + 5)∑n=140(0.1Tn+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.