NZ Level 7 (NZC) Level 2 (NCEA)
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Steady state solutions to recurrence relations

Interactive practice questions

The recurrence relations defining four different sequences are plotted below.

Which sequences approach a steady-state solution as $n$n becomes large? Select all correct answers.

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A

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B

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C

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D

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A

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B

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C

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D
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We can define the term values of a sequence by a recurrence relation of the form $t_{n+1}=rt_n+d$tn+1=rtn+d, where $t_1=a$t1=a.

If $-11<r<1, then the term values approaches a steady-state solution in the long term, when $n$n becomes large.

Consider the recurrence relation $t_{n+1}=0.2t_n+8$tn+1=0.2tn+8 where $t_1=-4$t1=4.

Consider the recurrence relation $t_{n+1}=-0.8t_n-18$tn+1=0.8tn18 where $t_1=3$t1=3.

Outcomes

M7-3

Use arithmetic and geometric sequences and series

91258

Apply sequences and series in solving problems

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