DAY 4 Introduction to sequences. PI 11ArithmeticAndGeom.notebook DAY 4 February 20, 2017 February 17/18, 2017 Did you Copy notes on FACTORIALS? CLASS OPENER (Do NOW): UNIT 8: Sequences and Series PI11: Arithmetic and Geometric Sequences. Apr 104:46 PM Feb 118:33 AM U8: PI 11 Arithmetic and Geometric Sequences REVIEW: Writing numbers using expressions Use variables to write : FIND THE MISSING TERMS IN THE SEQUENCE GIVEN BELOW Any integer An Even integer An Odd integer Three consecutive integers Three consecutive odd integers _____; _____; an ; _______; _______ Three consecutive even integers Any two odd integers back in time ...... in algebra Given two points (2, 4) ; (3 , 5) find the slope : an=an1 + 18 in present time ....... given a sequence of 5 terms 2, 4, 6, 8, 10 how would you identify each term using variables ? an+1=an+18 Apr 104:54 PM Apr 104:55 PM Definition of a SEQUENCE: Definition of a SEQUENCE: A sequence is an ordered list of numbers. Each member of a sequence is called a term. Terms of a sequence are arranged in a pattern. A formula that defines the terms of the sequence is called an explicit formula. A sequence is an ordered list of numbers. Each member of a sequence is called a term. Terms of a sequence are arranged in a pattern. A formula that defines the terms of the sequence is called an explicit formula. EX 2. Write the first four terms of a sequence given by the explicit formula: EX 2. Write the first four terms of a sequence given by the explicit formula: n an PER C n an Apr 104:55 PM Apr 104:55 PM 1 DAY 4 Introduction to sequences. PI 11ArithmeticAndGeom.notebook February 20, 2017 PER. A Apr 148:59 AM Apr 148:59 AM A sequence can also be defined by a recursive formula. Find the first four terms in each sequence given the formula. a) b) 1 With a recursive formula, one or more previous terms are used to generate the next term and one or more first terms must be known. [You may have seen a type of recursive formula called "NOW/NEXT" statements in the past] EX 4. Write the first five terms of a sequence given by a recursive formula a2= a3 = a4= a5 = Apr 21:50 PM EX.5.: The Fibonacci sequence is defined recursively as follows: Write the first 6 terms of this sequence. Apr 104:58 PM Apr 104:58 PM Explicit and Recursive Formula Find the next three terms in each sequence and write the recursive and explicit formula for the given sequence. -5 , -1, 3, 7, ... 0, 3, 8, 15, 24, ... Apr 104:58 PM 2 DAY 4 Introduction to sequences. PI 11ArithmeticAndGeom.notebook Explicit and Recursive Formula Find the next three terms in each sequence and write the recursive and explicit formula for the given sequence. February 20, 2017 Explicit and Recursive Formula Find the next three terms in each sequence and write the recursive and explicit formula for the given sequence. 0, 3, 8, 15, 24, ... -5 , -1, 3, 7, ... 0, 3, 8, 15, 24, ... Apr 211:17 AM Apr 104:58 PM Find the next three terms in a sequence given and find the nth term formula for each sequence : Find the next three terms in a sequence given and find the nth term formula for each sequence : 1 , 1 , 3 , 1, 5 , ... 2 2 8 4 32 1 , 1 , 3 , 1, 5 , ... 2 2 8 4 32 Feb 279:10 AM Feb 279:10 AM Which sequence is finite and which one is infinite 1 , 4, 7, 10, ..., an=3n-2, ... 1 , 4, 7, 10, ...,28 Feb 269:43 PM Mar 172:19 PM 3 DAY 4 Introduction to sequences. PI 11ArithmeticAndGeom.notebook Mar 172:19 PM Arithmetic Sequence February 20, 2017 Mar 172:20 PM PI 11: Lesson 8.1. - 8.2. Finding terms of a sequence and Arithmetic Sequences >>>PRACTICE sheet Additional practice: >>>Section 8.1: Page 563/ 15, 17, 21, 23, 45, 47, 49, 51, 55, 59, 63, 65, 71, 73 >>>Section 8.2: Page 573/ 5, 13, 15, 21, 25, 31, 37, 41 Mar 172:21 PM Mar 172:16 PM 4
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