1. Review of Recursive Rules:
Review of Arithmetic Sequences:
A sequence formed by adding a fixed number to a term to find the next number.
The fixed number is called the ________________________.
Example: 2, 5, 8, 11, …
Create a “table of values” from the sequence.
Find the common difference. Find the initial value where n = 0.
Write an explicit rule for the sequence.
(similar to linear function notation)
Geometric Sequences:
A sequence formed by multiplying a term in the sequence by a fixed number to find the next term.
The fixed number is called the _______________________.
Example: 2, , , , …
Find the common ratio. Use the first term as the initial value.
(similar to exponential function notation except the common ratio is raised to the (n-1) power instead of to the n power)
Review of Recursive Rules:
Remember:
n = now (current)
n – 1 = previous
Recursive rules always tell us two things:
The first term f(1)
How you get the rest of the terms in the sequence
f(n) = f(n-1) …
* Make sure to include what you are going to do to the “previous term” to get the “current term” and what values of n to use (Ex. n>2 or n>1).
Arithmetic Sequences:
Write a recursive rule for the Arithmetic Sequence to the left.
Geometric Sequences:
Write a recursive rule for the Geometric Sequence to the left.
common difference
common ratio

2. Tell whether each sequence is an arithmetic or geometric sequence
Tell whether each sequence is an arithmetic or geometric sequence. Find the common difference or common ratio.
Write an EXPLICIT RULE and a RECURSIVE RULE for each. Find f(12) in each sequence (the 12th term).
M.C. problems taken from Alg1 Sem1 Practice Exam