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Sequences and Series

Sequences and Series

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Question 144

The population of a bacteria colony, PnP_nPn​ (in thousands), at the start of day nnn is modelled by the recurrence relation

Pn+1=A−BPn P_{n+1} = A - B P_n Pn+1​=A−BPn​ P1=6 P_1 = 6 P1​=6

where AAA and BBB are constants.

a.

Find, in terms of AAA and BBB, (i) P2P_2P2​ (ii) P3P_3P3​

[2]
b.

Given that

  • ∑n=13Pn=50\sum_{n=1}^{3} P_n = 50∑n=13​Pn​=50
  • A=2B+8A = 2B + 8A=2B+8

Show that 2B2−5B−14=02B^2 - 5B - 14 = 02B2−5B−14=0.

[4]
c.

Hence find the smaller possible value of P2P_2P2​.

[2]
Markscheme

Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /Sequences and Series

178 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.

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