Lesson 1: Sequences

• Defining a Sequence and a Term

• Worked examples determining a sequence, given the formula

• Worked examples for generating a formula for the nth term

  • Examples for finding the nth term

• Recursive Sequences

• Defining a recursive sequence

• Solutions to finding recursive sequences

Lesson 2: Arithmetic Sequence

• Defining an Arithmetic Sequence

• General formula for an arithmetic sequence:

  • Terms explained

• Examples solving various types of arithmetic sequences questions:

  • Solving for the next n terms, given the first set of terms

  • Solving for the first n terms, given arithmetic sequence

  • Solving for the formula for the nth term

  • Solving for the number of terms in an arithmetic sequence

  • Solving for the first term and formula for the nth term

Lesson 3: Geometric Sequences

• Defining a Geometric Sequence

• General formula

  • Explanation of terms

• Examples of solutions to geometric sequences questions

  • Solving for Common Ratio and next 3 terms

  • Solving for first 4 terms, given formula for the nth term

• Solving for tη

Lesson 4: Arithmetic Series

• Defining arithmetic series

• Differentiating between arithmetic sequences & arithmetic series

• General formula for arithmetic series

  • Explanation of terms

• Examples of solutions to arithmetic series questions:

  • Solving for the sum of the first n terms

  • Solving for the sum of an arithmetic series

Lesson 5: Geometric Series

• Defining geometric series

• Differentiating between geometric sequences & geometric series

• General formula for geometric series

  • Explanation of terms

• Examples of solutions to geometric series questions:

  • Solving for the sum of the first n terms

  • Solving for the sum of a geometric series

Lesson 6: Binomial Expansion

• Pascal’s triangle and its interpretation

• Relationship of a cubic binomial with Pascal’s Triangle

• General relationship of (x + y)n to Pascal's Triangle

• 4 properties of a Binomial Expansion of the form (x+y)n

• Examples of expanding binomials using Pascal’s Triangle

Here are a few sample questions for you to practice. The answers are given at the end.