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)
326 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.