Download Day 5 Arith. sequences

Sequences and Series
Alana Poz
Sequence

Sequence – ordered progression
of numbers
 There is always a rule or the ability
to generate a rule to describe a
sequence
Difference Between Arithmetic
and Geometric Sequences

Arithmetic Sequence – the terms have a
common difference
 The difference between each term will always
be the same and is the amount between each
term
○ Ex) 5, 10, 15, 20… 30
 The difference, or d (constant), is always 5.

Geometric Sequence – the terms are found
by multiplying each preceding term by a
common ratio
 The common ratio is the number used to
multiply
○ Ex) 2, 4, 8, 16… 64
 The difference, or r (common ratio), is always 2.
Explaining “n”
n = index number
This means that whatever n equals, is the
placement of an in the sequence.
ex) 5, 10, 15, 20, 25
 When n = 1,
an =
5
 When n = 3, an = 15
 When n = 5, an = 25
Recursive Formulas *used to find next term
 Arithmetic
Recursive Formula
 an = an–1 + d
○an = # in the series
○an–1 = preceding term
Practice Recursive Formulas
ex) Given: 10, 12, 14… Find the next term.
1. Use Formula: a1 = 10
an = an–1 + d
1. Find d: What is the difference between each
term? 2 , so 2 is the common difference, d
2. Plug into formula: an = 14 + 2 = 16
(an–1 = 14 because it is the preceding term to the
next missing term)
3. What are the next 3 terms?
Explicit Formulas
*used to calculate any number in the sequence
 Arithmetic
Explicit Formula
 an = a1 + (n - 1)d
We need to know a1 and d. Then
we can find an any value of n!
What if n = 100???
Practice Explicit Formulas
 Arithmetic
Practice
ex) Given: -7, -1, 5, 11… Find n = 25
1. Use formula: an = a1 + (n - 1)d
2. Plug in values: an = -7 + (25-1)6
3. Simply: an = -7 + 150 – 6
4. Result: 137
Series = Sum of a Sequence
 Arithmetic
Summation Formula
 This formula calculates the sum
of a finite series.
n/2 (a1 + an)
Practice Summation Formulas
 Arithmetic
Practice
ex) Given: 117, 110, 103… 33
sum.
Find
1. Use formula: an = a1 + (n – 1)d
2. Plug in values: an = 117 + (n – 1)7
3. Simplify: an = 124 – 7n
4. Solve for n: 33 = 124 – 7n  n =
13
Now for some practice!