The temperature of a specialized metal alloy at the end of stage nnn of a cooling process is denoted by TnT_nTn, measured in Kelvin. The process is modeled by the recurrence relation
Tn+1=ωTn+84 T_{n+1} = \omega T_n + 84 Tn+1=ωTn+84where T1=1200T_1 = 1200T1=1200 and ω\omegaω is a constant.
Find an expression, in terms of ω\omegaω, for T2T_2T2.
It is given that the temperature at the end of the third stage is T3=822T_3 = 822T3=822.
Show that ω\omegaω satisfies the equation
200ω2+14ω−123=0 200\omega^2 + 14\omega - 123 = 0 200ω2+14ω−123=0It is given that the sequence of temperatures is a decreasing sequence. Find the value of T4T_4T4 and the value of T5T_5T5.
The limit of TnT_nTn as n→∞n \to \inftyn→∞ is LLL.
Write down an equation for LLL.
Find the value of LLL.
178 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.