1. Lesson 4.1: Identifying & Graphing Sequences Essential Question: What is a sequence and how are sequences and functions related?

2. Vocab
Sequence = a list of numbers in a specific order. Term = each element/number in a sequence. Explicit Rule = a way to specific term without finding the previous terms. Usually involves “plugging in”. Recursive Rule = defines a term by relating it to the value of a previous term.

3. Find the 1st Four Terms Using an Explicit Rule
Rule: 3n2 + 1

4. Find the nth Terms Using an Explicit Rule
Rule: n2 – 5; term 6 Rule: 4n - 3; term 11

5. Recursive Rule: Math: f(1) = 4 f(n) = f(n-1) + 10
Words: first term is 4
next term: add 10 to previous answer

6. Recursive Rule: Math: f(1) = 3 f(n) = f(n-1) + 5
Words: first term is _________
next term: add ___ to previous answer n
F(n)

7. Find the 1st 5 terms of the sequence
f(1) = 35 and f(n) = f(n - 1) – 2
f(1) = 45 and f(n) = f(n – 1) - 4

8. A pizza place is having a special
A pizza place is having a special. If you order a large pizza for a regular price of $17, you can order any number of additional pizzas for $8.50 each. Use the recursive rule f(1) = 17 and f(n) = f(n – 1) for each whole number n greater than 1. n
F(n)

9. A gym charges $100 as the membership fee and $20 monthly fee
A gym charges $100 as the membership fee and $20 monthly fee. Use the explicit rule f(n) = 20n to construct and graph the sequence. n
F(n)