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1.6.7 Generate a sequence by formula or recurrence (A-level only)

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Question 21

The population of a bacteria colony, $P_n$ (in thousands), at the start of day $n$ is modelled by the recurrence relation

P_{n+1} = A - B P_n

P_1 = 6

where $A$ and $B$ are constants.

Find, in terms of $A$ and $B$ , (i) $P_2$ (ii) $P_3$

[2]

Given that

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

Show that $2B^2 - 5B - 14 = 0$ .

[4]

Hence find the smaller possible value of $P_2$ .

[2]

Markscheme

1.6.7 Generate a sequence by formula or recurrence (A-level only) Questions

A Level
Maths
1.6.7 Generate a sequence by formula or recurrence (A-level only)

35 exam-style questions on OCR (MEI) A Level Maths 1.6.7 Generate a sequence by formula or recurrence (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

1.6.7 Generate a sequence by formula or recurrence (A-level only)

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1.6.7 Generate a sequence by formula or recurrence (A-level only)

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Question 21

The population of a bacteria colony, $P_n$ (in thousands), at the start of day $n$ is modelled by the recurrence relation

P_{n+1} = A - B P_n

P_1 = 6

where $A$ and $B$ are constants.

Find, in terms of $A$ and $B$ , (i) $P_2$ (ii) $P_3$

[2]

Given that

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

Show that $2B^2 - 5B - 14 = 0$ .

[4]

Hence find the smaller possible value of $P_2$ .

[2]

Markscheme

1.6.7 Generate a sequence by formula or recurrence (A-level only) Questions

A Level
Maths
1.6.7 Generate a sequence by formula or recurrence (A-level only)

35 exam-style questions on OCR (MEI) A Level Maths 1.6.7 Generate a sequence by formula or recurrence (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.