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

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.

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

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

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

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)

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

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) + 8.5 for each whole number n greater than 1. n F(n)

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 + 100 to construct and graph the sequence. n F(n)