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VCE 12 General 2023

5.01 First order recurrence relations

Interactive practice questions

Consider the sequence represented in the table.

$n$n $5$5 $6$6 $7$7 $8$8 $9$9
$x_n$xn $-23$23 $-27$27 $-31$31 $-35$35 $-39$39
a

What type of sequence is this?

Arithmetic

A

Geometric

B
b

Find the next element of the sequence.

That is, find $x_{10}$x10.

Easy
< 1min

Complete the sequences with the given conditions below.

Easy
1min

Consider the recurrence relation $u_{n+2}=u_{n+1}+u_n$un+2=un+1+un.

Complete the table for the first $10$10 terms in the sequence when $u_1=1$u1=1 and $u_2=1$u2=1.

Medium
2min

Consider the sequence defined by $a_0=3$a0=3 and $a_{n+1}=a_n-6$an+1=an6 for $n\ge0$n0.

Easy
4min
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Outcomes

U3.AoS2.1

the use of first-order linear recurrence relations to model growth and decay problems in financial contexts

U3.AoS2.5

model and analyse growth and decay in financial contexts using a first-order linear recurrence relation

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