Unit 3

📈 Sequences & Finance

Patterns in numbers, growth over time, and how money works. From arithmetic sequences to compound interest and loans, these skills connect directly to real life and appear throughout the exam.

7 subtopics

7 of 7 ready to study now 🎉

Links to Unit 4 financial topics

New to this topic? Start with Arithmetic Sequences, they're the simplest pattern and everything else builds from there. Geometric sequences and compound interest are closely related, so they click once you've got the basics.

Sequences

Arithmetic Sequences

Patterns that go up or down by the same amount each time. Find the nth term, the sum, and work backwards from given information.

common difference nth term t_n = a + (n−1)d sum formula

Geometric Sequences

Patterns that multiply by the same ratio each step, like population growth, compound interest, or radioactive decay.

common ratio t_n = arⁿ⁻¹ growth & decay sum formula

Recurrence Relations

Define a sequence by referring to the previous term. The same tool that models loan repayments, investments and depreciation, once you get this, all the finance topics unlock.

t_n+1 = r·t_n + d first-order recurrence starting value fixed additions

Financial Mathematics

Compound Interest

Interest calculated on both the principal and accumulated interest. The formula, the multiplier, and solving for n or r given other values.

A = P(1 + r/n)^nt growth multiplier compounding periods effective rate

Reducing Balance Loans

How home loans and car loans actually work, interest charged on what you still owe, reducing with each repayment.

recurrence relation outstanding balance repayment amount total interest paid

Regular deposits into an investment, like saving for retirement. Interest compounds AND you keep adding money each period.

V_n+1 = R·V_n + d regular deposits recurrence relation total interest earned

Earth Geometry & Time

Calculate the time difference between cities around the world. Add when travelling east, subtract when heading west. Covers UTC offsets, AEST/AEDT and international flight times.

UTC offset AEST / AEDT east = add west = subtract flight arrivals

Test Yourself, Escape Rooms

Training Log, Escape Room

6 challenges covering arithmetic sequences: common difference, nth term, sum formula, solving for n, finding a, and working from two terms.

The Lab Report, Escape Room

6 challenges covering geometric sequences: common ratio, nth term, sum formula, solving for n, growth from two terms, and working backwards to find r.

The Score Tracker, Escape Room

6 challenges covering recurrence relations: generating terms, arithmetic type, geometric type, and financial sequences with both r and d.

First Home, Escape Room

6 challenges on reducing balance loans: period interest, closing balances, repayment schedules, and total interest paid.

The Nest Egg, Escape Room

6 challenges covering annuities: generating terms with the recurrence relation, second account scenario, total interest earned, and the loan vs savings sign change.

The World Clock, Escape Room

6 challenges covering time zones: city-to-city conversions, negative offsets, flight arrival times with UTC conversion, and the LA-to-Brisbane 15-hour gap.

Road Trip, Escape Room

6 challenges covering Sequences, Compound Interest, Reducing Balance Loans, Time Zones and Recurrence Relations. Plan the road trip to escape.