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1.7 D: Sequences and series

1.7 D: Sequences and series

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Question 204

A sequence of daily depth changes in a reservoir, x1,x2,x3,…x_1, x_2, x_3, \dotsx1​,x2​,x3​,…, is defined by the recurrence relation

xn+1=2(xn+2)2−10 x_{n+1} = 2(x_n + 2)^2 - 10 xn+1​=2(xn​+2)2−10 x1=k−2 x_1 = k - 2 x1​=k−2

where kkk is a constant.

a.

Find an expression for x2x_2x2​ in terms of kkk, giving your answer in simplest form.

[2]
b.

Given that ∑n=13xn=k+22\sum_{n=1}^{3} x_n = k + 22∑n=13​xn​=k+22

find the possible values of x2x_2x2​.

[5]
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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