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1.7 D: Sequences and series

1.7 D: Sequences and series

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Question 170

A robotic arm moves along a linear track. Its position pnp_npn​ (in cm) at step n n\,n is governed by the recurrence relation:

pn+1=3−(pn)2 p_{n+1} = 3 - (p_n)^2 pn+1​=3−(pn​)2
a.

In the case where the arm starts at p1=2p_1 = 2p1​=2:

(i) Find the value of p3p_3p3​.

(ii) Determine the value of p100p_{100}p100​.

[4]
b.

State a different value for p1p_1p1​, other than p1=2p_1 = 2p1​=2, which gives the same value for p100p_{100}p100​ as found in part (a)(ii).

[2]
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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