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.
231 exam-style questions on WJEC A Level Maths 3.4 Sequences and Series (A-level only), covering 3.4.1 Sequences and Series (A-level only), 3.4.2 Sequences and Series (A-level only), 3.4.3 Sequences and Series (A-level only), 3.4.4 Sequences and Series (A-level only), 3.4.5 Sequences and Series (A-level only), 3.4.6 Sequences and Series (A-level only), and 3.4.7 Sequences and Series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.