# 6.04 Practical applications of arithmetic sequences

Lesson

### Applications of arithmetic sequences

In Chapter 3, linear functions were applied to examples of linear growth and decay. As seen in the last lesson of this chapter, arithmetic sequences can also be used to model linear growth. Hence, arithmetic sequences can be applied in many areas of life, including simple interest earnings, straight-line depreciation, monthly rental accumulation and many others.

For example, when someone is saving money in equal instalments, the cumulative savings at each savings period form an arithmetic sequence. If the driver of a vehicle is travelling down a highway at a constant speed, the amount of petrol left in the tank, measured every minute of the trip, forms another arithmetic sequence. In fact, any time a quantity is changing by equal amounts at set time periods, the process can be considered as being arithmetic and therefore represented by an arithmetic sequence.

#### Worked example

##### Example 1

Tabitha starts with $\$200$$200 in her piggy bank, the following week she adds \25$$25 and then continues to add $\$25$$25 at the start of each successive week. Find a rule to describe B_nBn the balance of her savings at the start of each week and find when her savings will reach \450$$450.

### Outcomes

#### AoS3.12

Define and explain key concepts in use of a first-order linear recurrence relation to generate the terms of a number sequence, and apply a range of related mathematical routines and procedures

#### AoS3.15

Define and explain key concepts in use of a recurrence relation to model and analyse practical situations involving discrete linear growth or decay such as a simple interest loan or investment, the depreciating value of an asset using the unit cost method; and the rule for the value of a quantity after n periods of linear growth or decay and its use, and apply a range of related mathematical routines and procedures