A sequence y1,y2,y3,… y_1, y_2, y_3, \dots\,y1,y2,y3,… is defined by
y1=cyn=5yn−1−2,n≥2 \begin{aligned}y_1 &= c \\y_n &= 5y_{n-1} - 2, \quad n \geq 2\end{aligned} y1yn=c=5yn−1−2,n≥2Find an expression for y2 y_2\,y2 in terms of ccc.
Show that y3=25c−12y_3 = 25c - 12y3=25c−12.
Find ∑r=14yr\sum_{r=1}^4 y_r∑r=14yr in terms of ccc.
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.