The depth of water in a tidal sensor tank, dnd_ndn mm, measured at the start of each hour nnn, is modeled by the recurrence relation
dn+1=P−Qdn d_{n+1} = P - Q d_n dn+1=P−Qdnwhere PPP and QQQ are constants and d1=6d_1 = 6d1=6.
Find expressions in terms of PPP and QQQ for (i) d2d_2d2 (ii) d3d_3d3
Given that ∑n=13dn=60\sum_{n=1}^{3} d_n = 60∑n=13dn=60 and P=5Q+8P = 5Q + 8P=5Q+8
Show that Q2−4Q−38=0Q^2 - 4Q - 38 = 0Q2−4Q−38=0.
Hence find the smaller possible value of d2d_2d2, giving your answer in the form a−ba - \sqrt{b}a−b where aaa and bbb are integers.
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.
