A sequence u1,u2,u3,… u_1, u_2, u_3, \dots\,u1,u2,u3,… is defined by
u1=pun=2un−1−3,n≥2 \begin{aligned}u_1 &= p \\u_n &= 2u_{n-1} - 3, \quad n \geq 2\end{aligned} u1un=p=2un−1−3,n≥2Find an expression for u2 u_2\,u2 in terms of ppp.
Show that u3=4p−9u_3 = 4p - 9u3=4p−9.
Find ∑r=14ur\sum_{r=1}^4 u_r∑r=14ur in terms of ppp.
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.
