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.
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.