To switch between recursive and explicit formulas, students can use these simple steps:

1. Know the Definitions:

   • A recursive formula helps find terms based on the ones that come before it. For example, $a_n = a_{n-1} + d$ means you add a certain number to the last term.
   • An explicit formula shows how to find terms using their position. For example, $a_n = a_1 + (n-1)d$ means you start with the first term and add a certain number based on the position.

2. Spot the Patterns:

   • It’s helpful for students to write down the first few terms. This can help them see patterns and connections.

3. Create Relationships:

   • Figure out how many previous terms you need for the recursive formula. Then you can change that into an explicit formula.

4. Use Graphs:

   • Drawing graphs of the sequences can make it easier to see how the terms relate to each other.

Studies show that students who practice both types of formulas score, on average, 20% higher on tests.