A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1,x2,x3,… is defined by
x1=1xn+1=axn+6,n≥1 \begin{aligned}x_1 &= 1 \\x_{n+1} &= ax_n + 6, \quad n \geq 1\end{aligned} x1xn+1=1=axn+6,n≥1Find an expression for x2 x_2\,x2 in terms of aaa.
Show that x3=a2+6a+6x_3 = a^2 + 6a + 6x3=a2+6a+6.
Given that x3=22x_3 = 22x3=22, find the possible values of aaa.
308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.