A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1,x2,x3,… is defined by
x1=5xn+1=pxn−6,n≥1 \begin{aligned}x_1 &= 5 \\x_{n+1} &= px_n - 6, \quad n \geq 1\end{aligned} x1xn+1=5=pxn−6,n≥1Find an expression for x2 x_2\,x2 in terms of ppp.
Show that x3=5p2−6p−6x_3 = 5p^2 - 6p - 6x3=5p2−6p−6.
Given that x3=21x_3 = 21x3=21, find the possible values of ppp.
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.