Skip to content
MathsGenie logo
Quick links
Open app

Course home

  1. A Level
  3. Maths AQA
  5. Question bank

1.7.2 Types of sequence (A-level only)

EasyMedium
12345678910111213141516171819202122232425
Question 22

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]

1.7.2 Types of sequence (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.7.2 Types of sequence (A-level only)