In this lesson, you learned how to:

• Explain why different equations can represent the same sequence.

Here are the activities that helped you reach those goals:

• 4.18.1 Repeated Operations
  • In this activity, you looked at different ways to represent repeated addition with multiplication and exponents.
• 4.18.2 Identifying Domain for a Function
• 4.18.3 Define an Arithmetic Sequence by the $n^{\text{th}}$ Term
  • In this activity, you learned how to represent arithmetic sequences using an explicit general rule.
  • 4.18.3: Self Check
  • 4.18.3: Additional Resources
• 4.18.4 Define a Geometric Sequence by the $n^{\text{th}}$ Term
  • In this activity, you learned how to represent geometric sequences using an explicit general rule.
  • 4.18.4: Self Check
  • 4.18.4: Additional Resources
• 4.18.5 Interchanging between Formulas
  • In this activity, you learned that arithmetic and geometric sequences can be written using the recursive definition and the $n^{\text{th}}$ term. It is possible to use them interchangeably.
  • 4.18.5: Self Check
  • 4.18.5: Additional Resources
• 4.18.6 Different Types of Equations
  • In this activity, you looked at how the same arithmetic sequence was represented recursively and with the $n^{\text{th}}$ term.

After these activities, you completed the following practice:

• 4.18.7 Practice