A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1,x2,x3,… is defined by
x1=kxn=4xn−1−1,n≥2 \begin{aligned}x_1 &= k \\x_n &= 4x_{n-1} - 1, \quad n \geq 2\end{aligned} x1xn=k=4xn−1−1,n≥2Find, in terms of kkk, the values of x2x_2x2, x3 x_3\,x3 and ∑r=14xr\sum_{r=1}^4 x_r∑r=14xr.
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.