What is wrong sign for depreciation?

Flat-rate depreciation has a negative common difference because the value falls each year.

WAMathematics ApplicationsSyllabus dot point

How do we model situations that change by a constant amount each step?

Recognise arithmetic sequences, use the recursive and explicit rules, and apply them to simple interest and linear depreciation.

How to identify an arithmetic sequence by its common difference, use the recursive and explicit term rules, and apply them to simple interest and flat-rate depreciation.

Generated by Claude Opus 4.76 min answerUpdated 2026-05-29

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
The common difference
Where arithmetic sequences appear
Choosing recursive or explicit

What this dot point is asking

You must recognise arithmetic behaviour, use both the recursive and explicit forms, find any term, and apply the model to simple interest and straight-line depreciation.

The common difference

A sequence is arithmetic when each term differs from the one before by the same constant, the common difference $d$ . A positive $d$ gives steady growth (a straight line rising), a negative $d$ steady decline.

The explicit rule jumps straight to any term without listing the ones before it, which is why it is preferred for the later terms.

Where arithmetic sequences appear

The arithmetic model fits any quantity that changes by a fixed amount per period.

Simple interest. Interest is a fixed amount each period because it is always calculated on the original principal, so the balance grows arithmetically.
Flat-rate (straight-line) depreciation. An asset loses the same dollar amount each year, so its value falls arithmetically.

Worked example

Simple interest as an arithmetic sequence

\ $5000 is invested at$ 6% $simple interest per year. The interest each year is$ 6% $of \$ 5000 = \ $300, a fixed amount, so the balance is arithmetic with$ a = 5000 $and$ d = 300$.

Recursive rule: $t_{n+1} = t_n + 300$ , $t_1 = 5300$ (balance after one year).

Explicit rule for the balance after $n$ years: $t_n = 5000 + 300n$ .

Balance after $8$ years: $t_8 = 5000 + 300 \times 8 = 5000 + 2400 = 7400$ , that is $7400.

Because the interest is always $300, the balance climbs by equal steps, the hallmark of simple interest and of every arithmetic model.

Choosing recursive or explicit

Use the recursive rule when generating a table term by term or when technology iterates for you. Use the explicit rule when asked for a single far-off term, such as the value after $30$ years, because it avoids listing every step.