• Mathematics Advanced
  • Year 12

Series and Applications

approx. 8 hrs

7 topics

22 concepts

Enrol in Series and Applications to master the algebraic techniques involved in series and its application to financial mathematics.

Available in


In this learning program students will investigate arithmetic and geometric series. We will help students effectively derive and apply rules to solve a range of differentiated questions. Students will gain confidence working with the application of series to solve financial problems, including time payments and superannuation.

Topics & Concepts We Cover

This learning program is made up of the following 7 topics, broken down into 22 concepts.

  • General Series 1 concept

    1. Derive a formula for the nth term of a series

  • Sigma Notation 3 concepts

    1. Use sigma notation to determine number of terms in a series

    2. Convert from sigma notation to expanded form

    3. Convert from expanded form to sigma notation

  • Arithmetic Series 3 concepts

    1. Sum of an arithmetic progression

    2. Find the nth term of an arithmetic sequence

    3. Identify that a sequence is an arithmetic sequence by finding a common difference

  • Finite Geometric Series 3 concepts

    1. Sum of a geometric series

    2. Identify that a sequence is a geometric sequence by finding the common ratio

    3. Find nth term of a geometric sequence

  • Infinite Geometric Series 3 concepts

    1. Finding the limiting sum of an infinite geometric series

    2. Finding the rational form of a recurring decimal using infinite geometric series

    3. Find the condition for an infinite geometric series to converge

  • Application of Series 4 concepts

    1. Miscellaneous application problems for arithmetic and geometric series

    2. Annuities applications

    3. Loan repayment applications

    4. Compound interest applications

  • Mathematical Induction 5 concepts

    1. Proving the closed form of a series using induction

    2. Proving divisibility using induction

    3. Proving the closed form of first-order recurrence using induction

    4. Principle of mathematical induction

    5. Proving inequalities using induction

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Series and Applications


  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

Ready to start this program?

Simply pick a time that works for you

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We'll be in contact to match you with one of our top tutors and book your first session

Starting at

$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime

Access to practice questions

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