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1.7 D: Sequences and series

1.7 D: Sequences and series

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Question 27
65%

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

1.7 D: Sequences and series Questions

  1. A Level
  2. /Maths
  3. /1.7 D: Sequences and series

308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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