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1.6.7 Generate a sequence by formula or recurrence (A-level only)

1.6.7 Generate a sequence by formula or recurrence (A-level only)

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Question 2
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A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1​,x2​,x3​,… is defined by

x1=3xn+1=axn−4,n≥1 \begin{aligned}x_1 &= 3 \\x_{n+1} &= ax_n - 4, \quad n \geq 1\end{aligned} x1​xn+1​​=3=axn​−4,n≥1​
a.

Find an expression for x2 x_2\,x2​ in terms of aaa.

[1]
b.

Show that x3=3a2−4a−4x_3 = 3a^2 - 4a - 4x3​=3a2−4a−4.

[2]
c.

Given that x3=11x_3 = 11x3​=11, find the possible values of aaa.

[3]
Markscheme

1.6.7 Generate a sequence by formula or recurrence (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.6.7 Generate a sequence by formula or recurrence (A-level only)

35 exam-style questions on OCR (MEI) A Level Maths 1.6.7 Generate a sequence by formula or recurrence (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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