### Concept (1)

While arithmetic and geometric sequences involve a rule that uses a constant number, recursion sequences use the terms themselves in the rule. One term in recursion sequences is determined from using the terms before it. This concept of recursion sequences can be difficult to fully comprehend, but is found often in mathematics. For example, the Fibonacci sequence is a famous recursion sequence.

### Sample Problems (6)

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Given a1 = 1, a2 = 2, and an = 2an−1 + an−2

Find the next three terms.
###### Problem 1
How to interpret a recursive formula.
###### Problem 2
How to generate terms of a number pattern from a recursive formula.
###### Problem 3
Determining whether given formulas are recursive or explicitly defined.
###### Problem 4
How to write both explicit and recursive formulas for the same number pattern
###### Problem 5
Finding the explicit formula, recursive formula, or both for a given number pattern.
###### Problem 6
Writing recursive formulas for given number patterns, and using the formula to find the next few terms.