A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1,x2,x3,… is defined by
x1=pxn=3xn−1+2,n≥2 \begin{aligned}x_1 &= p \\x_n &= 3x_{n-1} + 2, \quad n \geq 2\end{aligned} x1xn=p=3xn−1+2,n≥2Find an expression for x2 x_2\,x2 in terms of ppp.
Show that x3=9p+8x_3 = 9p + 8x3=9p+8.
Find ∑r=14xr\sum_{r=1}^4 x_r∑r=14xr in terms of ppp.
308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, 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). Each one has a worked solution and a mark scheme showing where the marks go.