1. School starts at 7:15 for EOCT testing!
May and May 17-20:
School starts at 7:15 for EOCT testing!
Sequences
EOCT: May 10-11

2. Vocabulary Sequence: an ordered list of numbers Ex. -2, -1, 0, 1, 2, 3
Term: each number in a sequence
Ex. a1, a2, a3, a4, a5, a6
Infinite Sequence: sequence that continues infinitely
Ex: 2, 4, 6, 8, …
Finite Sequence: sequence that ends
Ex: 2, 4, 6
Explicit Formula: defines the nth term of a sequence.

3. Example 1:
Write the first six terms of the sequence defined by an = 4n + 5
Write the first six terms of the sequence defined by an = 2n2 – 1

4. Vocabulary Recursive Formula: an-1
Uses one or more previous terms to generate the next term.
an-1

5. Example 2: A) Write the first six terms of the sequence
where a1 = -2 and an = 2an-1 – 1
B) Write the first six terms of the sequence where a1 = 4 and an = 3an-1 + 5

6. School starts at 7:15 for EOCT testing!
May and May 17-20:
School starts at 7:15 for EOCT testing!
Arithmetic Sequences
EOCT: May 10-11

7. Vocabulary Arithmetic Sequence: What is d? a2 – a1
A sequence generated by adding “d” a constant number to pervious term to obtain the next term.
This number is called the common difference.
What is d? a2 – a1
3, 7, 11, 15, … d = 4
8, 2, -4, -10, … d = -6

8. Formula for the nth term
Common difference
an = a1 + (n – 1)d
First term in the sequence
What term you are looking for
What term you are looking for

9. Example 1: d Find the 10th term of a1 = 7 and an = an-1 + 6

10. Example 2:
Find the 10th term of the arithmetic sequence where a3 = -5 and a6 = 16
Find the 15th term of the arithmetic sequence where a5 = 7 and a10 = 22
Find the 12th term of the arithmetic sequence where a3 = 8 and a7 = 20

11. Vocabulary Arithmetic Means: Terms in between 2 nonconsecutive terms
Ex. 5, 11, 17, 23, 29  11, 17, 23 are the arithmetic means between 5 & 29

12. Example 3: Find the 4 arithmetic means between 10 & -30

13. School starts at 7:15 for EOCT testing!
May and May 17-20:
School starts at 7:15 for EOCT testing!
Geometric Sequences
EOCT: May 10-11

14. Vocabulary Geometric Sequence: What is r?
A sequence generated by multiplying a constant ratio to the previous term to obtain the next term.
This number is called the common ratio.
What is r?
2, 4, 8, 16, … r = 2
27, 9, 3, 1, … r = 1/3

15. Formula for the nth term
First term in the sequence
an = a1rn-1
What term you are looking for
What term you are looking for
Common Ratio

16. Example 1 Find the 5th term of a1 = 8 and an = 3an-1

17. Example 2: Find a10 of the geometric sequence 12, 18, 27, 40.5, …
Find a7 of the geometric sequence where a1 = 6 and r = 4

18. ***Keep reviewing for your EOCT***
Homework
P.140 #1-16
P.145 #1-17
***Keep reviewing for your EOCT***
(May 10-11)

19. Warm up 1. Find the 8th term of the sequence defined by a1= –4 and
an= an-1+ 2
2. Find the 12th term of the arithmetic sequence in which
a4= 2 and a7= 6
3. Find the four arithmetic means between 6 and 26.
4. Find the 5th term on the sequence defined by a1= 2 and
an= 2an-1.

20. School starts at 7:15 for EOCT testing!
May and May 17-20:
School starts at 7:15 for EOCT testing!
Series (M2)
EOCT: May 10-11

21. Series Series: the sum of a sequence Summation Notation:
EX. (for the above series)

22. = _______ + _______ + _______ + _______
= ____ + _____ + _____ + _____ = _____

23. Not in packet!! Summation Properties
For sequences ak and bk and positive integer n:
Not in packet!!

24. Summation Formulas For all positive integers n: Constant Linear
Quadratic

25. Example 1:
Evaluate

26. Extra Example: (Not in packet)
Evaluate
Homework:
P.135 #18-24
*work on Benchmark Practice WS*

27. EOCT: May 10-11 Sequences and Series Test: May 18
May and May 17-20:
School starts at 7:15 for EOCT testing!
Arithmetic Series (M2)
EOCT: May 10-11
Sequences and Series Test: May 18

28. Formula for arithmetic series
Vocabulary
An Arithmetic Series is the sum of an arithmetic sequence.
Formula for arithmetic series
Sn=

29. Example 1: Find the series 1, 3, 5, 7, 9, 11
B. Find the series 8, 13, 18, 23, 28, 33, 38

30. Example 2: Given 3 + 12 + 21 + 30 + …, find S25

31. Example 3:
Evaluate

32. EOCT: May 10-11 Sequences and Series Test: May 18
May and May 17-20:
School starts at 7:15 for EOCT testing!
Geometric Series (M2)
EOCT: May 10-11
Sequences and Series Test: May 18

33. Formula for geometric series
Vocabulary
An Geometric Series is the sum of an geometric sequence.
Formula for geometric series
Sn=

34. Example 1:
Given the series …find S10 to the nearest tenth.

35. Example 2: n
Evaluate r a1

36. (Sequences and Series ARE ON the EOCT)
Homework
P. 141 #16-27
P. 145 #18-23
Study/Review for EOCT!
(Sequences and Series ARE ON the EOCT)

37. Infinite Geometric Series (M2)
May and May 17-20:
School starts at 7:15 for EOCT testing!
Infinite Geometric Series (M2)
Sequences and Series Test: May 18
Finals:
1st Period – May 21
2nd Period – May 24
6th Period – May 26

38. Formula for infinite geometric series
Vocabulary
An Infinite Geometric Series is a geometric series with infinite terms.
Formula for infinite geometric series
S =
If r <1 then the _______ can be found
If r >1 then the _______ cannot be found
SUM
SUM

39. Example 1:
Find the sum of the infinite geometric series …
Find the sum of the infinite geometric series …

40. Example 2:
Find the sum of the infinite geometric series below:

41. Example 3: NOT IN PACKET Write 0.2 as a fraction in simplest form.

42. Homework
P. 147 #32 – 45 (M2 – Purple)