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.
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.