13.2  Recursive Definitions
A recursive formula always uses the preceding term to define the next term of the sequence.  Sequences can have the same formula but because they start with a different number, they are different patterns.  1, 3, 5, 7, . . . and 2, 4, 6, 8, . . . have the same common difference but they are certainly not the same sequence because they have different starting values.  Point being, you must include the starting number in any recursive definition.

Sample of a recursive defintion:      19, 14, 9, 4, . . .
Initial condition:  t1 = 19  (look at the beginning)
Recursive formula:  tn = tn-1 - 5  ( each term is 5 less than the term before!)
Note:  Formulas in the previous section where explicit formulas!

Sample problems:

The answers:
That's about it for recursive definitions. ( bad pun, does recursive mean to curse again?)
Let's "sail" right along into the next section!