A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1,x2,x3,… is defined by
x1=2xn+1=axn−5,n≥1 \begin{aligned}x_1 &= 2 \\x_{n+1} &= ax_n - 5, \quad n \geq 1\end{aligned} x1xn+1=2=axn−5,n≥1Find an expression for x2 x_2\,x2 in terms of aaa.
Show that x3=2a2−5a−5x_3 = 2a^2 - 5a - 5x3=2a2−5a−5.
Given that x3=20x_3 = 20x3=20, find the possible values of aaa.
Practise Edexcel A Level Maths Sequences and Series with exam-style questions for A Level Maths. 100 questions 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, matched to the Edexcel A Level Maths (9MA0) 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.