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.
178 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.