3/5/2016Agenda Textbook / Web Based ResourceTextbook / Web Based Resource –Sequences –Factorials –Series –Sigma (Summation) Notation ClassworkClasswork INSERT HERE HomeworkHomework INSERT HERE

3/5/2016 Sequences and Summation Notation

3/5/2016 By the end of the day: You should know how to: Write the first 5 terms of a sequenceWrite the first 5 terms of a sequence Find a specific term of a sequenceFind a specific term of a sequence Find the ratio of factorialsFind the ratio of factorials Find a formula for the nth term of a sequenceFind a formula for the nth term of a sequence Find a sum from summation notationFind a sum from summation notation

3/5/2016Definitions Infinite Sequence: An endless list of numbers that follows a given rule Terms: The numbers in the sequence Finite Sequence: The first n terms in an infinite sequence

Sequences Sequence Notation: an (a sub n) means the nth (any) term of the sequence a1 (a sub 1) means the first term of the sequence a2 (a sub 2) means the second term and so on an = 4n + 1 gives you the rule for the sequence

Sequences a n = 4n + 1 Which ever term you are looking for, multiply that number by 4 and then add 1. a 1 = 4(1) + 1 = 5a 2 = 4(2) + 1 = 9 a 3 = 4(3) + 1 = 13a 15 = 4(15) + 1 = 61

3/5/2016Sequences When asked to find the formula look for 1 of 2 things: –The same number being added each time Determine what is being added (may be neg)Determine what is being added (may be neg) Multiply this number by “n”Multiply this number by “n” Add/Subtract a constant to make everything workAdd/Subtract a constant to make everything work –The same number being multiplied each time Determine what is being multiplied (may be neg)Determine what is being multiplied (may be neg) Raise this number to the “n-1” powerRaise this number to the “n-1” power Multiply by the first termMultiply by the first term

3/5/2016Sequences Find a formula for the nth term of the following sequence: 2, 5, 8, 11, 14, … 3, 6, 9, 12, 15, … + 3 each time

3/5/2016Sequences Find a formula for the nth term of the following sequence: 3, 6, 12, 24, 48, … 1, 2, 4, 8, 16, … x 2 each time

3/5/2016Sequences You Try These on Your Own: 1.INSERT YOUR PROBLEMS HERE

3/5/2016Factorials n! = n * (n – 1) * (n – 2) *... * 2 * 1n! = n * (n – 1) * (n – 2) *... * 2 * 1 0! = 1 (By Definition)0! = 1 (By Definition) 1! = 11! = 1 2! = 2 * 1 = 22! = 2 * 1 = 2 3! = 3 * 2 * 1 = 63! = 3 * 2 * 1 = 6 Multiply n by each integer less than it all the way down to 1Multiply n by each integer less than it all the way down to 1

3/5/2016 Dividing Factorials When dividing factorials, many things can cancel out: Pg 395 # 30, 32, 30) 32) 10

3/5/2016 Series - Definitions Series: The sum of the terms in a sequence. Infinite series: The sum of the terms of an infinite sequence Finite series: The sum of the terms of a finite sequence

3/5/2016 Sigma Notation Sigma Means: “the sum of”

3/5/2016 Sigma Notation Means: The sum of terms 1 through 5 of the sequence defined by 4i + 1

3/5/2016 Try These… 1)2)

3/5/2016 By the end of the day: Do you know how to: Write the first 5 terms of a sequence?Write the first 5 terms of a sequence? Find a specific term of a sequence?Find a specific term of a sequence? Find the ratio of factorials?Find the ratio of factorials? Find a formula for the nth term of a sequence?Find a formula for the nth term of a sequence? Find a sum from summation notation?Find a sum from summation notation?

3/5/2016Homework Study: INSERT HERE Do: Read & Take Notes: INSERT HERE

3/5/2016 Resource Credits Justin Bohannon Justin Bohannon Justin Bohannon