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Sequences and Series

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Question 122

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]

Sequences and Series Questions

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

Practise Edexcel A Level Maths Sequences and Series with exam-style questions for A Level Maths. 156 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank