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.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
