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3.3 Sequences and series (A-level only)

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Question 10
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A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1​,x2​,x3​,… is defined by

x1=kxn=4xn−1−1,n≥2 \begin{aligned}x_1 &= k \\x_n &= 4x_{n-1} - 1, \quad n \geq 2\end{aligned} x1​xn​​=k=4xn−1​−1,n≥2​
a.

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

[1]
b.

Show that x3=16k−5x_3 = 16k - 5x3​=16k−5.

[2]
c.

Find ∑r=14xr\sum_{r=1}^4 x_r∑r=14​xr​ in terms of kkk.

[3]
Markscheme

3.3 Sequences and series (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.3 Sequences and series (A-level only)

200 exam-style questions on CCEA A Level Maths 3.3 Sequences and series (A-level only), covering 3.3.1 Sequences and series (A-level only), 3.3.2 Sequences and series (A-level only), 3.3.3 Sequences and series (A-level only), 3.3.4 Sequences and series (A-level only), 3.3.5 Sequences and series (A-level only), 3.3.6 Sequences and series (A-level only), 3.3.7 Sequences and series (A-level only), and 3.3.8 Sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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