1. Sequences and Series
Arithmetic Sequences
Alana Poz

2. Sequence Sequence – ordered progression of numbers
There is always a rule or the ability to generate a rule to describe a sequence

3. 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.

4. Explaining “n” ex) 5, 10, 15, 20, 25 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

5. Recursive Formulas Arithmetic Recursive Formula an = an–1 + d
*used to find next term
Arithmetic Recursive Formula
an = an–1 + d
an = # in the series
an–1 = preceding term

6. Practice Recursive Formulas
ex) Given: 10, 12, 14… Find the next term.
Use Formula: a1 = 10
an = an–1 + d
Find d: What is the difference between each term? 2 , so 2 is the common difference, d
Plug into formula: an = = 16
(an–1 = 14 because it is the preceding term to the
next missing term)
What are the next 3 terms?

7. Explicit Formulas Arithmetic Explicit Formula an = a1 + (n - 1)d
*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???

8. Practice Explicit Formulas
Arithmetic Practice
ex) Given: -7, -1, 5, 11… Find n = 25
Use formula: an = a1 + (n - 1)d
Plug in values: an = -7 + (25-1)6
Simply: an = – 6
Result: 137

9. Series = Sum of a Sequence
Arithmetic Summation Formula
This formula calculates the sum of a finite series.
n/2 (a1 + an)

10. Practice Summation Formulas
Arithmetic Practice
ex) Given: 117, 110, 103… Find sum.
Use formula: an = a1 + (n – 1)d
Plug in values: an = (n – 1)7
Simplify: an = 124 – 7n
Solve for n: 33 = 124 – 7n  n = 13

11. Now for some practice!