ALGEBRA IICHAPTER 12

12.5: Use Recursive Rules with Sequences and Functions

HW: p.830-831 (4, 10, 14, 18, 20, 34)

EXPLICIT VS. RECURSIVE RULE Explicit rule gives an as a function of

the term’s position number n in the sequence.

Recursive rule gives the beginning term or terms of a sequence and then a recursive equation that tells how an is related to one or more preceding terms.

RECURSIVE EQUATIONS Arithmetic Sequence: an = an-1 + d

where d is the common difference.

Geometric Sequence: an = r an-1 where r is the common ratio.

WRITE THE FIRST SIX TERMS OF THE SEQUENCE.1.) a0 = 1, an = an-1 + 4

2.) a1 = 1, an = 3an-1

WRITE A RECURSIVE RULE FOR THE SEQUENCE.

1.) 3, 13, 23, 33, 43, …

2.) 16, 40, 100, 250, 625, …

3.) 1, 1, 2, 3, 5, …

EXTRA PRACTICE: WRITE A RECURSIVE RULE FOR THE SEQUENCE.

1.) 450, -150, 50, -50/3, …

2.) 11, 8, 5, 2, …