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 an expression for x2 x_2\,x2 in terms of kkk.
Show that x3=16k−5x_3 = 16k - 5x3=16k−5.
Find ∑r=14xr\sum_{r=1}^4 x_r∑r=14xr in terms of kkk.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) 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.
