A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1,x2,x3,… is defined by
x4=kxn=4xn+1−1,n≥1 \begin{aligned}x_4 &= k \\x_n &= 4x_{n+1} - 1, \quad n \geq 1\end{aligned} x4xn=k=4xn+1−1,n≥1Find an expression for x3 x_3\,x3 in terms of kkk.
Show that x2=16k−5x_2 = 16k - 5x2=16k−5.
Find ∑r=14xr\sum_{r=1}^4 x_r∑r=14xr in terms of kkk.
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.