Algebra II Chapter 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, …