1. Closed Sequences

2. Sequences
The values in the range are called the terms of the sequence.
Domain: …....n
Range: a1 a2 a3 a4….. an
A sequence can be specified by an equation or rule.

3. Find the first 5 Terms of the Sequence
an = 2n – 3
Find a1, a2, a3, a4, a5
a1 = -1 First Term
a2 = 1 Second Term
a3 = 3 Third Term
a4 = 5 Fourth Term
a5 = 7 Fifth Term

4. Find the first 5 Terms of the Sequence
an = n3 – 20
Find a1, a2, a3, a4, a5
a1 = First Term
a2 = Second Term
a3 = Third Term
a4 = Fourth Term
a5 = Fifth Term
-19
-12 7 44
105

5. Arithmetic Sequences will have a constant common difference.

6. Tell whether the sequence 2, 11, 20, 29, 38, … is arithmetic.
Yes because each common difference is 9.

7. Tell whether the sequence 4, 8, 16, 22, 32, … is arithmetic.
No because the difference is not constant.

8. Closed
Sequences

9. Write the rule
Example:
3, 5, 7, 9, ...
an = 2n + 1

10. Write the rule
Example:
65, 60, 55, 50, ...
an = -5n + 70

11. Write the rule
Example:
2, 6, 10, 14, …
an = 4n – 2

12. What is the 50th term? Example: 1, 5, 9, 13, ...
Substitute 50 in as an

13. What is the 18th term? Example: 100, 93, 86, 79...
Substitute 18 in as an

14. To Write a Recursive Rule
a1 = ___ an = an-1 d + -

15. Write the first 6 terms of the sequence
Write the first 6 terms of the sequence. Then state the domain and range
a1 = 3
an = -2an-1

16. Write a recursive rule for the following
38, 27, 16, 5, -4…

17. Write a recursive rule for the following
4, 8, 12, 16, 20…

18. RECURSIVE CLOSED an-1 n an = a1 +(n-1)d Need First Term
an = an-1 (+-x÷) P
a1 = ___
Plug in right side numbers n
an = a1 +(n-1)d