Reminding you that we have a quiz this Wednesday on:
- Arithmetic & Geometric Sequences
- Explicit and Recursive Definitions
Skills required:
- Finding the next term of a sequence
- Finding the nth term
- Understanding sequences as discrete functions
- Finding explicit (function) definitions given a few terms of a sequence
- Finding recursive definitions given a few terms of a sequence
Blog Prompt:
Review your notes 1st, otherwise you won't get much out of this.
Then respond to the following:
- What questions do you have on this topic?
- What mistakes are you most likely to make? (Since no one has earned a 100% on all of the quizzes, I expect thoughtful answers from all of you)
- Create a potential quiz problem on one of these topics. You will benefit most if you make this question on the topic for which you feel the least prepared. Add your solution, or attempted solution, as a comment so that others may compare their thoughts with yours. (If I get some good questions, then I will likely use some of them on the quiz)
Complete this assignment as soon as possible! The seniors and your classmates are waiting to help you but time runs out on Tuesday night.
6 comments:
mr. alcantara
i understand clearly how to find the sequences and the nth term using the two formulas we have, beacuse the formulas are clear and easy to follow. but i make mistakes finding the nth term when i dont have the first one, i copied in my notebook similar poroblems so i could practice for the quiz, so i gue i will be spending some time in these kinds of problems.
its somtimes hard for me yo find the recursive definitions given a few terms of a sequence.
continue...
the 3rd and 4th terms of an arithmetic sequence are 3.8, and 5.4.
1.find the recursive definition of the sequence.
2. find an explicit definition for the sequence.
1. ans=
* how many jumps? 20-4= 16 jumps
*total jumps? 5.4-3.8= 1.6
*size of jump= 1.6/16= .1
*t1=3.8-1.6(.1)
ans: t1=3.67
= tn=tn-1+.1------------>recursive
2. ans=
tn=t1+(n-1)
tn= 3.67+(n-1)(.1)
1. Mr. Alcantara:
I think I understand pretty well the Tepic on sequences(arithmetic and geometric), but even though I do, I got a little confused on the word problems like the one you did today in class about the laptop. I think I have to work more on those types of problems so I can be completely ready and secure for the quiz on Wednesday. I think the formulas have been very useful for me since it gives me a better understanding and easier way of the problems. I think I have a hard time to find formulas and values of a big number, without doing it the logical y repeatedly way. (For example the 40th term).
2. cont..
*Find the 7th term of the geometric sequence whose 2nd and 3rd terms are: …1.8,0.89
R= 0.89/1.8= .4944
tn= t1* r ^(n-1)
t7=3.6*.4944^(7-1)
t7= .052
1.8/t1(t1)=.4944(t1)
1.8/.4944=.4944/.4944
3.6=t1
1. What questions do you have on this topic?
I think I understand the topic well, and I am confident, but, I sometimes get confused when the sequence does not start in the first term.
What mistakes are you most likely to make?
I think the mistake I am most likely to make is to mix up the equation for Geometric and Arithmetic sequences. Or I will mix up what a recursive definition is and what an explicit definition is.
Create a potential quiz problem on one of these topics.
What is the 20th term for a geometric sequence whose 2nd term is 2.68 and third term is 3.72
Solution:
Geometric sequence formula:
Tn = T1 + r^(n-1)
r = 3.72 / 2.68 = 1.38805
T20 = 2.68 + 1.38805^(19-1)
368.5206737
1. This topic has been relieving while comparing it with some of the past, but as everything, it has some confusing parts. I personally think that some of the most confusing processes are when you have a word problem and they don’t tell if it is arithmetic or geometric, or when you read the problem and can’t figure out which one is the first term or how can you organize the information. What can you do first to organize the information of this kind of problems in an appropriate way?
2. As I mentioned in the first answer, I consider that I’m most likely to make a mistake when I read a problem and it’s just not clear enough for me to arrange the correct information in the right order.
3. Assume that an air conditioner gains 10% of its value every January. So when you buy one of this it will worth 10% more of its original value. If the cost is $5,000, what is its value 6 years later?
Then it would be more complicated if the question was, If the cost is n, how much will you earn in 6 years? or what is the value 6 years ago?
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