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VCE 11 General 2023

5.04 Applications of arithmetic sequences

Interactive practice questions

A paver needs to pave a floor with an area of $800$800 square metres. He can pave $50$50 square metres a day.

a

Complete the table showing the area left to pave at the start of each day:

Day Area of floor left to pave ($m^2$m2)
$1$1 $800$800
$2$2 $\editable{}$
$3$3 $\editable{}$
$4$4 $\editable{}$
$5$5 $\editable{}$
b

What type of change is this?

Linear growth

A

Exponential growth

B

Linear decay

C

Exponential decay

D
Easy
1min

The value of a fridge depreciates by a constant amount each year and is modelled by the recurrence relation

$V_{n+1}=V_n-300$Vn+1=Vn300, $V_0=1600$V0=1600

where $V_n$Vn is the value of the fridge, in dollars, after $n$n years.

Easy
1min

The value of Belem Bank shares is decreasing by $\$1.55$$1.55 each day.

At the beginning of today's trading, the shares are worth $\$48.83$$48.83.

Medium
3min

Skye is a salesperson and is paid a travel allowance of $\$40$$40 for each business trip she takes to demonstrate the use of the product she sells.

Each week she is also paid a retainer of $\$220$$220.

Medium
2min
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Outcomes

U1.AoS2.7

use a given recurrence relation to generate a sequence, deduce the explicit rule, n u from the recursion relation, tabulate, graph and evaluate the sequence

U1.AoS2.8

use a recurrence relation, table or graph to model and analyse practical situations involving discrete linear growth or decay

U1.AoS2.9

demonstrate the use of a recurrence relation to determine the linear depreciating value of an asset after 𝑛 time periods for the initial sequence

U1.AoS2.10

use a rule for the future value of a linear depreciating asset to solve practical problems

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