Algebra 1A - Explicit and Recursive Formulas

5 flashcards · Mathematics · by OctoBlast

1. There are two ways for finding terms in any sequence. You can find: any term (using the explicit formula) or the next term (using the recursive formula)

2. Either way, you start by finding the common difference.

3. The explicit formula: an=a1+(n−1)d a_n = a_1 + (n-1)d" role="presentation">an=a1+(n−1)dan=a1+(n−1)d a_n = a_1 + (n-1)dan=a1+(n−1)da_n = a_1 + (n-1)dan​=a1​+(n−1)d

4. The recursive formula: an=an−1+d a_n = a_{n-1} + d" role="presentation">an=an−1+dan=an−1+d a_n = a_{n-1} + dan=an−1+da_n = a_{n-1} + dan​=an−1​+d

5. A recursive formula for sequences always defines a1 a_1" role="presentation">a1a1 a_1a1a_1a1​ and then defines an using the term before it, an−1 a_{n-1}" role="presentation">an−1an−1 a_{n-1}an−1a_{n-1}an−1​