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3.7 Recurrence Relations

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Question 14

The temperature of a specialized metal alloy at the end of stage $n$ of a cooling process is denoted by $T_n$ , measured in Kelvin. The process is modeled by the recurrence relation

T_{n+1} = \omega T_n + 84

where $T_1 = 1200$ and $ω\omega$ is a constant.

Find an expression, in terms of $ω\omega$ , for $T_2$ .

[1]

bi.

It is given that the temperature at the end of the third stage is $T_3 = 822$ .

Show that $ω\omega$ satisfies the equation

200\omega^2 + 14\omega - 123 = 0

[3]

bii.

It is given that the sequence of temperatures is a decreasing sequence. Find the value of $T_4$ and the value of $T_5$ .

[4]

ci.

The limit of $T_n$ as $\to \infty$ is $L$ .

Write down an equation for $L$ .

[1]

cii.

Find the value of $L$ .

[1]

Markscheme

3.7 Recurrence Relations Questions

A Level
Maths
3.7 Recurrence Relations

35 exam-style questions on Edexcel A Level Maths 3.7 Recurrence Relations. Each one has a worked solution and a mark scheme showing where the marks go.

3.7 Recurrence Relations

Question bank

3.7 Recurrence Relations

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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 14

The temperature of a specialized metal alloy at the end of stage $n$ of a cooling process is denoted by $T_n$ , measured in Kelvin. The process is modeled by the recurrence relation

T_{n+1} = \omega T_n + 84

where $T_1 = 1200$ and $ω\omega$ is a constant.

Find an expression, in terms of $ω\omega$ , for $T_2$ .

[1]

bi.

It is given that the temperature at the end of the third stage is $T_3 = 822$ .

Show that $ω\omega$ satisfies the equation

200\omega^2 + 14\omega - 123 = 0

[3]

bii.

It is given that the sequence of temperatures is a decreasing sequence. Find the value of $T_4$ and the value of $T_5$ .

[4]

ci.

The limit of $T_n$ as $\to \infty$ is $L$ .

Write down an equation for $L$ .

[1]

cii.

Find the value of $L$ .

[1]

Markscheme

3.7 Recurrence Relations Questions

A Level
Maths
3.7 Recurrence Relations

35 exam-style questions on Edexcel A Level Maths 3.7 Recurrence Relations. Each one has a worked solution and a mark scheme showing where the marks go.