1. Factorials and Sequences
Sequences and Series
Factorials and Sequences

2. Factorials
Factorials are numbers that are found by using the products of consecutive numbers.
What does that mean?
1 * 2 * 3 * 4 = 24
In factorial notation, this would be 4!
Try one:
7! 5! 3!
Now use the calculator.
Press the number. (7)
<Math>; Arrow over to PRB; Option 4
<Enter> (5040)

3. Factorials Remember 7! = 1 * 2 * 3 * 4 * 5 * 6 * 7
We can use this information to simplify.
8! 5! = 336
1∗2 ∗ 3 ∗ 4 ∗ 5 ∗ 6 ∗7 ∗ 8 1 ∗ 2 ∗ 3 ∗ 4 ∗ 5
6 * 7 * 8
336
Try a couple.
6! 4! 9! 7! ! 8! 5! 8!
Expand the factorial.
Cancel out the numbers that are the same.
Multiply what is left.

4. Sequences
Sequence means to follow one thing after another in a certain order.
Same thing in math.
We need to know the notation of sequence in order to work with it.
𝑎 𝑛 = 2n – 1 is a sequence.
𝑎 𝑛 is the name of the sequence
2n – 1 is the operation needed to satisfy the sequence.
Notice the “n”? It is the same number for both.

5. Sequences Find the first 4 terms of the sequence.
(That means n = 1; n = 2; n = 3; n = 4)
𝑎 𝑛 = 2n – 1
𝑎 1 = 2(1) – 1
= 2 – 1
= 1
𝑎 2 = 2(2) – 1
= 4 – 1
= 3
𝑎 3 = 2(3) – 1
= 6 – 1
= 5
𝑎 4 = 2(4) – 1
= 8 – 1
= 7
Plug each of the n values into the sequence and solve.
(1, 3, 5, 7)

6. Sequences 𝑎 𝑛 = (−1) 𝑛 𝑛+1 Try a harder one: 𝑎 1 = (−1) 1 1+1 = −1 2
𝑎 𝑛 = (−1) 𝑛 𝑛+1
𝑎 1 = (−1)
= −1 2
𝑎 2 = (−1)
= 1 3
𝑎 3 = (−1)
= −1 4
𝑎 4 = (−1)
= 1 5
( −1 2 , 1 3 , −1 4 , 1 5 )

7. Sequences Sometimes you only need to find one term.
You know which one based on the “n” value asked for.
𝑎 𝑛 = 𝑛 (𝑛+1) 2 , 𝑎 15 = ?
𝑎 15 = 15 (15+1) 2
= =