2. 4 3 2 1 0
In addition to level
3.0 and above and
beyond what was
taught in
class, the student
may:
· Make connection
with other
concepts in math
· Make connection
with other content
areas.
The student will build a
function (linear and
exponential) that models a
relationship between two
quantities. The primary
focus will be on arithmetic
and geometric sequences.
- Linear and exponential
functions can be
constructed based off a
graph, a description of a
relationship and an
input/output table.
- Write explicit rule for a
sequence.
- Write recursive rule for a
sequence.
The student will
be able to:
- Determine if
a sequence is
arithmetic or
geometric.
- Use explicit
rules to find a
specified term
(nth) in the
sequence.
With help from
the
teacher, the
student has
partial success
with building a
function that
models a
relationship
between two
quantities.
Even with help,
the student has
no success
understanding
building
functions to
model
relationship
between two
quantities.
Focus 7 Learning Goal – (HS.F-BF.A.1, HS.F-BF.A.2, HS.F-LE.A.2, HS.F-IF.A.3) =
Students will build a function (linear and exponential) that models a relationship
between two quantities. The primary focus will be on arithmetic and geometric
sequences.
3. ARITHMETIC SEQUENCE
In an Arithmetic Sequence the difference
between one term and the next term is a
constant.
We just add some value each time on to infinity.
For example:
1, 4, 7, 10, 13, 16, 19, 22, 25, …
This sequence has a difference of 3 between each
number.
It’s rule is an = 3n – 2.
4. ARITHMETIC SEQUENCE
In general, we can write an arithmetic sequence
like this:
a, a + d, a + 2d, a + 3d, …
a is the first term.
d is the difference between the terms (called
the “common difference”)
The rule is:
xn = a + d(n-1)
(We use “n-1” because d is not used on the 1st
term.)
5. ARITHMETIC SEQUENCE
For each sequence, if it is
arithmetic, find the common
difference.
1. -3, -6, -9, -12, …
2. 1.1, 2.2, 3.3, 4.4, …
3. 41, 32, 23, 14, 5, …
4. 1, 2, 4, 8, 16, 32, …
1. d = -3
2. d = 1.1
3. d = -9
4. Not an arithmetic
sequence.
6. ARITHMETIC SEQUENCE
Write the explicit rule for the
sequence
19, 13, 7, 1, -5, …
Start with the formula: xn = a +
d(n-1)
a is the first term = 19
d is the common difference: -6
The rule is:
xn = 19 - 6(n-1)
Find the 12th term of this
sequence.
Substitute 12 in for “n.”
x12 = 19 - 6(12-1)
x12 = 19 - 6(11)
x12 = 19 – 66
x12 = 19 - 6(12-1)
x12 = -47
7. GEOMETRIC SEQUENCE
In a Geometric Sequence each term is found
by multiplying the pervious term by a
constant.
For example:
2, 4, 8, 16, 32, 64, 128, …
The sequence has a factor of 2 between each
number.
It’s rule is xn = 2n
8. GEOMETRIC SEQUENCE
In general we can write a geometric
sequence like this:
a, ar, ar2, ar3, …
a is the first term
r is the factor between the terms (called the
“common ratio”).
The rule is xn = ar(n-1)
We use “n-1” because ar0 is the 1st term.
9. GEOMETRIC SEQUENCE
For each sequence, if it is
geometric, find the common
ratio.
1. 2, 8, 32, 128, …
2. 1, 10, 100, 1000, …
3. 1, -1, 1, -1, …
4. 20, 16, 12, 8, 4, …
1. r = 4
2. r = 1.1
3. r = -1
4. Not a geometric
sequence.
10. GEOMETRIC SEQUENCE
Write the explicit rule for the
sequence
3, 6, 12, 24, 48, …
Start with the formula: xn = ar(n-1)
a is the first term = 3
r is the common ratio: 2
The rule is:
xn = (3)(2)(n-1)
(Order of operations states that we would take care of exponents before you
multiply.)
Find the 12th term of this
sequence.
Substitute 12 in for “n.”
x12 = (3)(2)(12-1)
x12 = (3)(2)(11)
x12 = (3)(2048)
x12 = 6,144
11. GROUP ACTIVITY
Each group will receive a set of cards
with sequences on them.
Separate the cards into two columns:
Arithmetic and Geometric.
For each Arithmetic Sequence, find the
common difference and write an
Explicit Formula.
For each Geometric Sequence, find the
common ratio and write a Explicit
Formula.
