Algebra 2 Name
Chapter 11: Sequence and Series Block Date
Warm-Up:
Find the pattern and write the next three terms.
1. 2, 4, 6, 8, 10, , , pattern:
2. 1, 4, 9, 16, 25, , , pattern:
3. 3, 5, 7, 9, 11, , , pattern:
4. –2, 4, -8, 16, , , pattern:
5. , 1, , 2, , , pattern:
11.1 Notes
Domain: Range:
A sequence of events is
A sequence in math is a function/equation whose domain is consecutive integers.
* If the domain is not stated, it begins at 1.
Ex. 6, 9, 12, 15, … Ex. ,…
Equation an = 3n + 3 Equation an =
n / 1 / 2 / 3 / 4 / 5 / 6 / … / 14 / … / nan
n / 1 / 2 / 3 / 4 / 5 / 6 / … / 14 / … / n
an
a1 means the 1st number in the sequence
a2 means the 2nd number in the sequence
a3 means the 3rd number in the sequence
.
.
.
a14 means the 14th number in the sequence
an means the nth number in the sequence
Practice: Write the first 5 terms of the sequence. Then find a12.
1. an = -4n +3 2. an = (-1)n+1 3. an = 5n –3
a1 = -4(1)+3 = -1 a4 = a1 = a4 = a1 = a4 =
a2 = -4(2)+3 = -5 a5 = a2 = a5 = a2 = a5 =
a3 = a12 = a3 = a12 = a3 = a12 =
4. an = n – 2 5. an = 2n 6. an = (-1)n
a1 = a4 = a1 = a4 = n
a2 = a5 = a2 = a5 = a1 = a4 =
a3 = a12 = a3 = a12 = a2 = a5 =
a3 = a12 =
Sequence Formulas
Arithmetic
Same number added/subtractedd à # added (if d is negative it is subtraction)
a1 à 1st value /
Sequence an = a1 + d(n-1)
Sum Sn =
Geometric
Same number multiplied/dividedr à # multiplied (if r is <1 it is division)
a1 à 1st value /
Sequence an = a1 r(n-1)
Sum Sn = a1Finding the pattern… a.k.a. Writing the equation for the sequence
Write the next term in the sequence. Then write a rule for the nth term.
Model Ex.1, 4, 9, 16 , à 12, 22, 32, 42, à Equation an = n2
Now You Try:
1. 1, 2, 4, 8, 2. 2, 4, 6, 8, 3. , 1, , 2, 4. 4, 3, 2, 1,
Equation: Equation: Equation: Equation:
Practice: Write the rule for the following sequence then find a8.
1. 5, 7, 9, 11, 13, 15, … a1 = d or r = rule a8
2. 35, 30, 25, 20, … a1 = d or r = rule
a8
3. 2, 6, 18, 54, … a1 = d or r = rule
a8
4. 40, 20, 10, 5, , … a1 = d or r = rule a8
Series
A series is
You can only add numbers if there is a
Ex. 3, 5, 7, 9, 11 Ex. 3, 5, 7, 9, 11, …
Can be added Cannot be added
Write the rule for the following series
1. 3 + 5 + 7 + 9 + 11
Equation/Rule
Hint: Write the equation using a formula
Sum Notation S à pronounced sigma à means
Ex. =
In General:
Practice:
1. 2 + 5 + 8 + 11 + 14 2. 1 + 4 + 9 + 16
pattern pattern
rule rule
sum notation sum notation
Formulas for Special Series
1+1+…+1+1+1/ 1+2+3+4+5+6
/ 1+4+9+16+25+36+49
/ Any Arithmetic
/ Any Geometric
a1()
Find the sum of the following series.
1. 5, 6, 7, 8, 9, 10 2. 1, 1, 1, 1, 1, 1, 1 3. 6, 8, 10, 12, 14
4. 5. 6.
7. 8. 9.
10. 11. 12.
The formulas on the right hand side of this table are the only ones you will be given on your test.
Arithmetic
Same number added/subtractedd à # added (if d is negative it is subtraction)
a1 à 1st value /
Sequence an = a1 + (n-1) d
Sum Sn = n
Geometric
Same number multiplied/dividedr à # multiplied (if r is <1 it is division)
a1 à 1st value /
Sequence an = a1 r(n-1)
Sum Sn = a1()