Arithmetic Sequences
Find the common difference:
13, 16, 19, . . .
d = 3
Find the common ratio:
1, 2, 4, 8, . . .
r = 2
3 requirements:
1. first term
2. formula/rule
3. domain
How many requirements are there for an explicit definition? What are they?
2 requirements:
1. formula/rule
2. domain
What word is used to describe a data set where the values are distinct and separate?
discrete
Find the common difference:
28, 22, 16, . . .
d = -6
Find the common ratio:
32, -8, 2, . . .
r = -1/4
How do we say a1? What does it represent?
"a sub 1"
first term
What 2 things are already built into the FORMULA of an explicit definition?
first term
common difference/ratio
How would you describe a graph that is continuous?
Answers may vary
ex: a smooth curve where you can drag your finger without lifting it
Find the 5th term using the recursive definition provided:
a1 = 3, an = an-1 + 7, n ≥ 2
a5 = 31
Find the 4th term using the recursive definition provided:
a1 = 4, an = an-1 ⋅ 2, n ≥ 2
a4 = 32
Write the recursive definition for the given arithmetic sequence:
12, 15, 18, . . .
a1 = 12
an = an-1 + 3
n ≥ 2
Write the explicit definition for the given arithmetic sequence:
12, 15, 18, . . .
an = 12 + 3(n - 1)
n ≥ 1
Show an example of a graph that could represent an arithmetic sequence
discrete set of points in a linear pattern
Find the 11th term using the explicit definition provided:
an = 5 + 4(n - 1)
a9 = 45
Find the 8th term using the explicit definition provided:
an = 2 ⋅ (3)n-1
a8 = 4374
Write the recursive definition for the given geometric sequence:
5, 30, 180, . . .
a1 = 5
an = an-1 ⋅ 6
n ≥ 2
Write the explicit definition for the given geometric sequence:
5, 30, 180, . . .
an = 5 ⋅ (6)n-1
Show an example of a graph that could represent an exponential function
a continuous curve that expresses a multiplicative pattern