1. Chapter 11
Sequences and Series

2. 11.1
Arithmetic Sequences

3. Key Terms Sequence: an ordered list of numbers
1, 3, 5, 7, 9, ….
Terms: the numbers in the sequence
The 1st term in the sequence above is 1, 2nd is 3, 3rd is 5, etc
Arithmetic Sequence: a sequence in which each terms after the 1st is found by adding a constant
Common difference: the number added to each term in an arithmetic sequence

4. Arithmetic sequence Formula: an = a1 + (n – 1)d
an = specific term (nth term)
a1 = 1st term in the sequence
n = number of position for given term
d = common difference

5. Find the next four terms in the sequence.
-6, -2, 2,….
1.6, 1.1, 0.6, ….

6. Write an equation for the nth term
10, 7, 4, 1, …

7. Write an equation for the nth term
8, 17, 26, 35, …

8. The table shows typical costs for a construction company to rent a crane for one, two, three, and four months. If the sequence continues, how much would it cost to rent the crane for a year?
Months
Cost ($) 1
75,000 2
90,000 3
105,000 4
120,000
The construction company has a budget of $350,000 for crane rental. The job is expected to last 18 months. Will the company be able to afford the crane rental for the entire job? Explain.

9. Find the first 5 terms for the sequence described
Find the indicated term for the sequence
a1 = 2 d = 13
a1 = 20, d = 4, n = 81

10. Arithmetic Means
The terms between any two non-successive terms in an arithmetic sequence
Use the formula to find the common difference
Then use the common difference to calculate the arithmetic means

11. Find the arithmetic means between the given terms
16,__, __, __, __, 91, …
15.6, __, __, __, 60.4, ...

12. 11.2
Arithmetic Series

13. What is a series?
When the terms of a sequence are added, the indicated sum of the terms is called a series.
Example
Sequence 1, 2, 3, 4, 5, 6
Series

14. Sum of an Arithmetic Series

15. Find the sum of the series 7+12+17+22+…+52 n = 10

16. Find the sum of the first 50 positive even integers

17. Aiden did pushups every day in January
Aiden did pushups every day in January. He started on January 1st and increased the number of pushups done each day by 1. He did a total of 1085 pushups for the month. How many pushups did he do on the first day?

18. Find the first three terms a1 = 9 an = 105 Sn = 741
Step 1: plug in to find n
Step 2: plug in to find d
Step 3: use d to find the terms

19. Sigma Notation Compact form for series Uses the summation symbol Σ
Greek letter sigma

20. Sigma Notation formula for the sequence Last value of n
First value of n

21. Ex: For the sequence 1, 2, 3, 4, 5, 6 a1 = 1 d = 1 an = 1 + (n – 1)1

22. Find the sum 8
5-2n
n=1

23. Find the sum
150
11 + 2k
k=1

24. 11.3
Geometric Sequences

25. Geometric Sequence

26. Find the next two terms in the sequence
405, 135, 45,….
16, 24, 36, ….

27. Geometric Sequence Formula: an=a1rn-1

28. Find a term given the first term and the common ratio
a1 = r = -2
Find the eighth term

29. Write an equation for the nth term
432, 72,12, ….

30. Write an equation for the nth term
72, 56, 40, 24, …

31. Find a term given one term and the common ratio
a4 = r = 3
Find the tenth term.
aA3 = r = 4
Find the eighth term

32. Geometric Means
The terms between any two non-successive terms in a geometric sequence
Use the formula to find the common ratio
Then use the common ratio to calculate the geometric means

33. Find the geometric means
2.25, __, __, __, 576
Find the two geometric means between 4 and 13.5

34. 11.4
Geometric Series

35. Sum of a Geometric Series

36. Find the sum for the first 10 terms
a1 = 5, r = 4

37. Maria arranges some rows of dominoes so that after she knocks over the first one, each domino knocks over two more dominoes. If there are ten rows, how many dominoes does Maria use?

38. Evaluate

39. Find the first term in a series
S8 = 39, and r = 3

40. Find the sum of a geometric series for which