1. (C) Find the Sum of a sequence
Summation notation: Read as “sigma”
(ex) Find the sum.

2. Theorem on Sums:
Theorem on sum of a constant (c)
Theorem on sums
for every real number c

3. To determine if a sequence is arithmetic
(12 – 2) Arithmetic sequences
Learning targets:
To determine if a sequence is arithmetic
To Find a formula for an arithmetic sequence
To find the sum of an arithmetic sequence
Definition: An arithmetic sequence is defined recursively as
where d is the common difference.
(A) I do (ex) Show that the sequence is arithmetic 4, 6, 8, 10,…
and d = 2 n 1 2 3 4 an

5. We do (ex) Show that the sequence if arithmetic if
You do (ex) Show that the sequence if arithmetic if

6. <Try this> Work on #8 and 12 on page 821
(B) Find the particular term of an arithmetic sequence.
I do (ex) Find the forty-first tem of the arithmetic sequence:
2, 6, 10,14, 18, …
Step 1: Find
Step 2: Find using the formula.
Step 3: Find the required term.
nth term of an arithmetic sequence is found by

7. We do (ex) Find the term of the arithmetic sequence if
and
find
Step 1: Find d
Step 2: find using the formula.
Step 3: Find using the formula.
Step 4: find the required term.

8. You do (ex) Find the term of the arithmetic sequence if
and
Find
<Try this> #15, 27, and 29 on page 821

9. (C) Find the sum of an arithmetic sequence.
The sum of the first n term (nth partial sum of n term) Sn is given by: or
This means:
I do (ex) Find the sum: … + 120
Step 1: Find d : d = 4
Step 2: find the term of 120 using the formula.
Step 3: find the sum of the term using the formula.

10. We do (ex) Find the sum of all the even integers from through 100:
The sequence is 2, 4, 6, …, 100, ... n 1 2 3 4 an 6 8 Sn
Find an =
Find using the formula.

11. You do (ex) Find the partial sum of: 1 + 2 + 3 + 4 + …, + 1004…
100 an Sn
<Try this> #35, 42, and 43 on page 822

12. To show that a sequence is geometric
(12 – 3) geometric Sequences and Series
Learning targets:
To show that a sequence is geometric
To find a formula for geometric sequence
To find the sum of a geometric sequence
(A) Geometric Sequence

13. I do (ex) Find the nth term of the geometric sequence 2, 6, 18, 54, …, n3
4 … an 6 18
54 …
Fill in the table.
Find the common ratio.
Write the recursive formula for the sequence.
Find the 10th term of the sequence.

14. We do (ex) Find the nth term of the geometric sequence …, n1 2 3
4 … an …
Fill in the table.
Find the common ratio.
Write the recursive formula for the sequence.

15. You do: (ex) Write the nth term of the geometric sequence.
1, -6, 36, -216, … n 1 2 3
4 … an …
<try this> #25 and 28

16. (B) Geometric Series
Finite geometric series
Finite sum (partial sum) Sn of a geometric sequence with the first term a1 and a common ration r ≠ 1 is
This means n 1 2 3 4 an Sn
We also use the summation notation (sigma)

17. I do (ex) Find the sum of the first 7 terms of a geometric sequence.
-5, 15, -45, 135, … n 1 2 3 4… an Sn
Fill in the table, and find the common ratio.
Find the Sn

18. We do (ex) Find the sum of the first 6 terms of a geometric sequence.1 2 3 4… an Sn
Find the sum using a graphing calculator.
2nd
STAT
MATH
Sum(5)
STAT
OPS
Seq (5)
2nd
ENTER
½^(x-1),x,1,6,1))

19. You do (ex) Find the sum of the first 8 terms of a geometric sequence.
2, -4, 8, -16, … n 1 2 3 4… an Sn

20. (B-II) Infinite Geometric Series
Theorem:
If , then the infinite geometric series converges to the sum.
has the sum
Otherwise, an infinite geometric series diverges.

21. I do (ex) Determine if the geometric series converges or diverges
If converges, find the sum. n 1 2 3 4… an Sn
Find the common ratio.
Find the sum.

22. We do (ex) Determine if the geometric series converges or diverges=

23. You do (ex) Determine if the geometric series converges or diverges
<Try this> #51, 52, and 63 on page 831