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3.4 Sequences and Series (A-level only)

3.4 Sequences and Series (A-level only)

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Question 158

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

3.4 Sequences and Series (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.4 Sequences and Series (A-level only)

231 exam-style questions on WJEC A Level Maths 3.4 Sequences and Series (A-level only), covering 3.4.1 Sequences and Series (A-level only), 3.4.2 Sequences and Series (A-level only), 3.4.3 Sequences and Series (A-level only), 3.4.4 Sequences and Series (A-level only), 3.4.5 Sequences and Series (A-level only), 3.4.6 Sequences and Series (A-level only), and 3.4.7 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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