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1.4 Sequences and Series

1.4 Sequences and Series

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Question 215

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

1.4 Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /1.4 Sequences and Series

308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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