• 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
NSW

### Overview

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

Reporting

• 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

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