FOA/Algebra 1 Unit 4: Exponential Functions Notes
25
Day 7 Geometric Sequences
For the following patterns, find the next two numbers. Then describe the rule you are apply each time.
Rule Constant Ratio
________________________________ ______________
b. 192, 96, ________________________________ ______________
________________________________ ______________
________________________________ ______________
What did you notice about all of your patterns? ______________________________________________________
Sequences
A sequence is a pattern involving an ordered arrangement of numbers, geometric figures, letters, or other
objects. A sequence, in which you get the next consecutive term by multiplying or dividing a constant is called
a geometric sequence
constant value is called the constant ratio.
What you may not realize is when it comes to geometric sequences is that they are considered exponential
functions. The position of each term is called the term number or term position. We can think of the term
number or position as the input (domain) and the actual term in the sequence as the output (range). Instead of
using x for the input, we are going to use n and instead of using y for the output, we are going to use an.
Term Number (n)
Term (an) 1 6 36
Explicit Formula for Geometric Sequences
Explicit Formula:
a
n
= a
1
rn-1
1
st
Term
Constant Ratio
nth Term
