Melba copland secondary school

Name:Date:Period:Geometric Sequences —ZombiepocalypseSummary. When last we met, Zombies were taking over the world. We started Day Z with exactly one zombie. On each subsequent day, every zombie in existence turned exactly one human into a new zombie. The table below summarizes your findings.DayZombiesDayZombies1118131,0722219262,1443420524,28848211,048,576516222,097,152632234,194,304764248,388,60881282516,777,21692562633,554,432105122767,108,864111,02428134,217,728122,04829268,435,456134,09630536,870,912148,192311,073,741,8241516,384322,147,483,6481632,768334,294,967,2961765,536348,589,934,592Sequences. Weused a table to show our data. Another way to write this is as a sequence:Zombies={1⏟1stterm,2,4,8,16⏟5thterm,32,64,128,256,512⏟10thterm,1024,2048,4096,8192,16384⏟15thterm,...}Sequence Notation. Usually, mathematicians will use a single letter to denote their sequence. Let’s call ours 푍, for Zombies. We’re also going to use a subscript to refer to our terms:푍푛={1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384}Now, when we say 푍푛what we mean is “Tell me what the 푛thterm of 푍is.”For example, 푍10=512.Practice.1.푍5=2.푍17=3.푍30=4.If 푍푛=64, what is the value of 푛?5.If 푍푛=8,192, what is the value of 푛?6.How many totalzombies are there on day 10?Defining a Sequence using a Recursive Equation.Sometimes, it makes sense to write out an equation for your sequence. This makes it easier to find values and to share your work with others.A
recursive equation gives you a way to find the next value of a sequence if you already know the one before it.You already found out that the terms of our sequence double every time. In other words, the next term isalwaystwice as big as the one before it.7.The 12thterm is twice as big as which term?8.If the current term is the 15thterm, what term came before it?9.If the current term is the 10thterm, what term came before it?10.If the current term is the 20thterm,what term came before it? Write your answer as a subtraction problem.11.If the current term is the 푛th term, what term came before it? Write your answer as a subtraction problem.Writing a Recursive Equation. We want to write an equation that says: “The 푛th term is two times bigger than the term before it.” Use problem 11 to help you write a recursive equation for our zombie sequence.푍푛=Now let’s make the Zombiepocalypse even worse. Pretend that we still start with one zombie, but instead of only eating once per day, now our zombie eats three times per day.This means that each zombie will turn 3 humans into zombies every day.12.Write a new sequence, 퐻푛(for Hungry zombies). Remember to use curly braces around your sequence.Compute at least the first ten terms.13.Write a recursive equation to find 퐻푛in terms of 퐻푛−114.Use your resursive formula to find 퐻15.15.How does 퐻15compare to 푍15? Which islarger? How much larger is it?