Introduction to Sequences 17 May 2011

Get Up!!!

Definition Sequence – An ordered list of (generally) numbers Each number in the list is called a term of the sequence.

Application Knowing the rule of a sequence allows us to predict terms!!!

Other Examples of Sequences Green, Yellow, Red, … I pledge allegiance… {2, 4, 6, 8, 10, …}

Practice Determine the rule for the sequence AND find the next three terms: My country, ‘tis of thee… Red, Orange, Yellow, Green, … (ROY G…) –4, 3, 10, 17, … 1, 1, 2, 3, 5, 8, …

Fibonacci Sequence {1, 1, 2, 3, 5, 8, …} Fibonacci Sequence in Lateralus by Tool

Vocab. u 1 – 1 st term in the sequence u 2 – 2 nd term in the sequence u n – n th term in the sequence u n-1 – n-1 th term in the sequence

Practice Find the u 1 and the u 2 for each of the following sequences: My country, ‘tis of thee… Red, Orange, Yellow, Green, … (ROY G…) {–4, 3, 10, 17, …} {1, 1, 2, 3, 5, 8, …}

Recursive Form of a Sequence 1. You are given u 1 (the 1 st term) 2. You are given a formula for finding the n th term

Defining a Sequence Recursively {2, 5, 8, 11, 14, …}

Defining a Sequence Recursively, cont. {–7, –4, –1, 2, 5, …}

Defining a Sequence Recursively, cont. {¼, ½, 1, 2, 4, …}

Your Turn: For the following sequences, find u 1 and define the sequence recursively. {–6, –4, –2, 0, 2, …} {–4, –8, –16, –32, –64, …} {6, 11, 16, 21, 26, …} {8, 4, 2, 1, ½, ¼, …}

Finding Terms Using the Recursive Form u 1 = –7u n = u n–1 + 3 for n ≥ 2 Find the first 5 terms Find the 10 th term

Finding Terms Using the Recursive Form, cont. u 1 = 5u n = 3u n–1 – 2 for n ≥ 2 Find the first 5 terms Find the 10 th term

Your Turn: Find the first 5 terms AND the 10 th term for the sequences below: u 1 = 4 and u n = 2u n–1 + 3 for n ≥ 2 u 1 = 5 and u n = ⅓u n–1 – 4 for n ≥ 2