A sequence a1,a2,a3,… a_1, a_2, a_3, \dots\,a1,a2,a3,… is defined by
a1=qan=5an−1+3,n≥2 \begin{aligned}a_1 &= q \\a_n &= 5a_{n-1} + 3, \quad n \geq 2\end{aligned} a1an=q=5an−1+3,n≥2Find an expression for a2 a_2\,a2 in terms of qqq.
Show that a3=25q+18a_3 = 25q + 18a3=25q+18.
Find ∑r=14ar\sum_{r=1}^4 a_r∑r=14ar in terms of qqq.
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.