1. Sequences and Series
9.1

2. Sequence A set of numbers, determined by some function
infinite if the domain of that function is all positive integers
finite if the domain of that function consists of the first n
integers.

3. Writing the Terms of a Sequence
Write the first four terms of the sequence given by: 𝑎 𝑛 =3𝑛−2 𝑎 𝑛 =3+(−1 ) 𝑛

4. Alternating Sign
Find the first four terms:
𝑎 𝑛 = (−1) 𝑛 2𝑛+1

5. Find the Pattern Find the nth term of the sequence:
1,3,5,7,… 2,−5, 10, −17,…

6. Recursive Sequence
Write the first four terms of the sequence defined by: 𝑎 1 =3 𝑎 𝑘 =2 𝑎 𝑘−1 +1, 𝑘≥2

7. Fibonacci Sequence
Write a recursive rule for the Fibonacci Sequence 1, 1, 2, 3, 5, 8, 13, …

8. Factorial
n! = 1 x 2 x 3 x 4 x … x (n-1) x n

9. Summation Notation
𝑖=1 𝑛 𝑎 1 + 𝑎 2 + 𝑎 3 +…+ 𝑎 𝑛−1 + 𝑎 𝑛 Plug in for i starting with 1 and finishing with n and add all of the results. Evaluate: 𝑖=1 5 3𝑖 𝑥=0 6 𝑥 2 −1

10. Series The sum of terms of a sequence
The sum of the first n terms is called the nth partial sum
𝑖=1 𝑛 𝑎 𝑖 = 𝑎 1 + 𝑎 2 + 𝑎 3 +…+ 𝑎 𝑛−1 + 𝑎 𝑛
The sum of all terms of a sequence is called an infinite series
𝑖=1 ∞ 𝑎 𝑖 = 𝑎 1 + 𝑎 2 + 𝑎 3 +…

11. Find the sum Find (a)the third partial sum and (b) the sum of
𝑖=1 ∞ 𝑖

12. Homework
p. 613: 9, 13, 23, odd, odd, 70, odd