Tentative Assignments for Sequences and Series
Wednesday, 4-24: Sequences: Pg. 587: V1 – V9, 17, 25, 31, 33, 37, 39-43, 45, 49, 53, 55, 61, 63, 67, 75, 87, 97, 103, 107, 113, 115, 117, 121, 133, 145
Thursday, 4-25: Arithmetic Sequences: Pg. 598: 6, 7, 15, 21, 31, 37, 41, 45, 53, 59, 65, 71, 82, 84, 87, 89, 91, 93, 95
Friday, 4-26: Geometric Sequences: Pg. 607: 7, 9, 17, 23, 25, 31, 39, 41, 45, 49, 55, 61, 63, 69, 73, 79-82, 87, 97, 99, 101 – 107 odd
Here is the powerpoint I showed in class today.
Monday, 4-29: Worksheet on Powers, Harmonics, Fibonacci, etc.,
Pg. 618: 43 – 55 odd These should be the answers to the successive difference worksheet and I believe that these are the
answers to the harmonic worksheet.
Tuesday, 4-30: Worksheet on Powers, Harmonics, Fibonacci, etc., Foerster’s WS #1
Pg. 618: 43 – 55 odd These should be the answers to the successive difference worksheet and I believe that these are the
answers to the harmonic worksheet..
Wednesday, 5-1: Mathematical Induction: Pg. 617: 7-24 odds, Sequence Lab, Foerster’s WS #1
Here are samples of the induction proofs.
Thursday, 5-2: Mathematical Induction: Pg. 617: 7-24 evens, Sequence Lab, Foerster’s WS #1
Here are samples of the induction proofs.
Friday, 5-3: Induction Quiz #1: Foerster Problems WS #2, telescoping, etc.
I've decided to put a few other (4) other questions about induction on this quiz so the proof isn't all there is...
Today we discovered a beautiful relationship between trig and exponential functions. Although each class had different ideas, we all came to the same conclusions. Last year's synopsis is here. Here is a synopsis of your class discussions. The homework is to complete the second part (the conclusions) of the power series and to study for a quiz. Here are some solutions to that worksheet. This COULD be on your quiz:
Part I. Given a sequence:
A) Identify what type of sequence this is (arithmetic, geometric, harmonic, quadratic, Fibonacci, binomial*, other),
B) Write its nth term (recursively or explicitly),
C) Write its 50th (or whatever) term.
Part II. Given a series: (arithmetic, geometric, nested radical, nested fraction or super simple other)
Note:This may be written in summation notation.
A) If it is finite, find its sum. (arithmetic, geometric, nested radical, nested fraction or super simple other)
B) If it is infinite, does the series converge? If so, what to?
Part III. Insert means (geometric, arithmetic, harmonic).
Monday, 5-6: Induction Quiz #1: Foerster Problems WS #2, telescoping, etc.
I've decided to put a few other (4) other questions about induction on this quiz so the proof isn't all there is...
Today we discovered a beautiful relationship between trig and exponential functions. Although each class had different ideas, we all came to the same conclusions. Last year's synopsis is here. Here is a synopsis of your class discussions. The homework is to complete the second part (the conclusions) of the power series and to study for a quiz. Here are some solutions to that worksheet. This COULD be on your quiz:
Part I. Given a sequence:
A) Identify what type of sequence this is (arithmetic, geometric, harmonic, quadratic, Fibonacci, other),
B) Write its nth term (recursively or explicitly),
C) Write its 50th (or whatever) term.
Part II. Given a series: (arithmetic, geometric, nested radical, nested fraction or super simple other)
Note:This may be written in summation notation.
A) If it is finite, find its sum. (arithmetic, geometric, nested radical, nested fraction or super simple other)
B) If it is infinite, does the series converge? If so, what to?
Part III. Insert means (geometric, arithmetic, harmonic).
Tuesday, 5-7: Vector/Parametric Review Yes, we went outdoors and collected data for 2 labs. They are due Tuesday.
Here is a quiz review of sorts...
Answers to the Special Sequences Worksheet: 1. (1 + sqrt(17))/2 2. 9 3. (1 + sqrt(33))/2 4. (27 + sqrt(53))/2
5. (-3 + sqrt(21))/2 6. 2 7. (3 + sqrt(13))/2 8. 5
Wednesday, 5-8: Quiz and Review: Pg. 651: 1 – 95 eoo (137-144) and from your Foerster text pg. 762: problems 14, 15, 17, 18, 19, 21, 22
Thursday, 5-9: Quiz and Review: Pg. 651: 1 – 95 eoo, (137-144) and from your Foerster text pg. 762: problems 14, 15, 17, 18, 19, 21, 22
I assigned problem # 19 from your text was because it involved an investigation of the Golden Ratio (phi). The reason I want you to do this is because several of you have asked how to find the explicit form of the Fibonacci sequence. Well here is a pretty decent explanation of that, but until you realize that the ratio of successive terms of the Fibonacci sequence converge to phi, you don't know why they assume that the Fibonacci sequence is related to a geometric one.
Friday, 5-10 Sequence Review
Monday, 5-13 Test on Sequences/Sequence lab due
MAKE SURE YOU HAVE DATA FOR BOTH LABS DUE THIS WEEK!!
I CAN'T TAKE MAKE-UP WORK AFTER FRIDAY!
Tuesday, 5-14: Review/Parametric and Vector labs due for 1st period
Here is the parametric activity we did today.
Wednesday, 5-15 Review/Vector lab due for 2nd period
Here are review sheets made by Emily last year. Thank her for these!
Trig Identities Trig Applications 2D Vectors Parametrics Polar 3D Vectors Sequences
Her final exam review is on my blog, but here are more problems to work. They aren't too challenging, but they may help
you remember important concepts.
Thursday, 5-16 Review/Parametric lab due for 2nd period
Friday, 5-17 Retest Opportunity - LAST DAY FOR MAKE-UP WORK!
Monday, 5-20 FINAL EXAM
Friday, 4/13: We took a quiz Wednesday, got an Interesting Sequence to investigate,and looked at Mathematical Induction on Thursday. Today the Interesting Sequence tasks were due and the assignment this weekend is to complete an investigation of the Golden Ratio (phi). The reason I want you to do this is because several of you have asked how to find the explicit form of the Fibonacci sequence. Well here is a pretty decent explanation of that, but until you realize that the ratio of successive terms of the Fibonacci sequence converge to phi, you don't know why they assume that the Fibonacci sequence is related to a geometric one.
Wednesday, 4-24: Sequences: Pg. 587: V1 – V9, 17, 25, 31, 33, 37, 39-43, 45, 49, 53, 55, 61, 63, 67, 75, 87, 97, 103, 107, 113, 115, 117, 121, 133, 145
Thursday, 4-25: Arithmetic Sequences: Pg. 598: 6, 7, 15, 21, 31, 37, 41, 45, 53, 59, 65, 71, 82, 84, 87, 89, 91, 93, 95
Friday, 4-26: Geometric Sequences: Pg. 607: 7, 9, 17, 23, 25, 31, 39, 41, 45, 49, 55, 61, 63, 69, 73, 79-82, 87, 97, 99, 101 – 107 odd
Here is the powerpoint I showed in class today.
Monday, 4-29: Worksheet on Powers, Harmonics, Fibonacci, etc.,
Pg. 618: 43 – 55 odd These should be the answers to the successive difference worksheet and I believe that these are the
answers to the harmonic worksheet.
Tuesday, 4-30: Worksheet on Powers, Harmonics, Fibonacci, etc., Foerster’s WS #1
Pg. 618: 43 – 55 odd These should be the answers to the successive difference worksheet and I believe that these are the
answers to the harmonic worksheet..
Wednesday, 5-1: Mathematical Induction: Pg. 617: 7-24 odds, Sequence Lab, Foerster’s WS #1
Here are samples of the induction proofs.
Thursday, 5-2: Mathematical Induction: Pg. 617: 7-24 evens, Sequence Lab, Foerster’s WS #1
Here are samples of the induction proofs.
Friday, 5-3: Induction Quiz #1: Foerster Problems WS #2, telescoping, etc.
I've decided to put a few other (4) other questions about induction on this quiz so the proof isn't all there is...
Today we discovered a beautiful relationship between trig and exponential functions. Although each class had different ideas, we all came to the same conclusions. Last year's synopsis is here. Here is a synopsis of your class discussions. The homework is to complete the second part (the conclusions) of the power series and to study for a quiz. Here are some solutions to that worksheet. This COULD be on your quiz:
Part I. Given a sequence:
A) Identify what type of sequence this is (arithmetic, geometric, harmonic, quadratic, Fibonacci, binomial*, other),
B) Write its nth term (recursively or explicitly),
C) Write its 50th (or whatever) term.
Part II. Given a series: (arithmetic, geometric, nested radical, nested fraction or super simple other)
Note:This may be written in summation notation.
A) If it is finite, find its sum. (arithmetic, geometric, nested radical, nested fraction or super simple other)
B) If it is infinite, does the series converge? If so, what to?
Part III. Insert means (geometric, arithmetic, harmonic).
Monday, 5-6: Induction Quiz #1: Foerster Problems WS #2, telescoping, etc.
I've decided to put a few other (4) other questions about induction on this quiz so the proof isn't all there is...
Today we discovered a beautiful relationship between trig and exponential functions. Although each class had different ideas, we all came to the same conclusions. Last year's synopsis is here. Here is a synopsis of your class discussions. The homework is to complete the second part (the conclusions) of the power series and to study for a quiz. Here are some solutions to that worksheet. This COULD be on your quiz:
Part I. Given a sequence:
A) Identify what type of sequence this is (arithmetic, geometric, harmonic, quadratic, Fibonacci, other),
B) Write its nth term (recursively or explicitly),
C) Write its 50th (or whatever) term.
Part II. Given a series: (arithmetic, geometric, nested radical, nested fraction or super simple other)
Note:This may be written in summation notation.
A) If it is finite, find its sum. (arithmetic, geometric, nested radical, nested fraction or super simple other)
B) If it is infinite, does the series converge? If so, what to?
Part III. Insert means (geometric, arithmetic, harmonic).
Tuesday, 5-7: Vector/Parametric Review Yes, we went outdoors and collected data for 2 labs. They are due Tuesday.
Here is a quiz review of sorts...
Answers to the Special Sequences Worksheet: 1. (1 + sqrt(17))/2 2. 9 3. (1 + sqrt(33))/2 4. (27 + sqrt(53))/2
5. (-3 + sqrt(21))/2 6. 2 7. (3 + sqrt(13))/2 8. 5
Wednesday, 5-8: Quiz and Review: Pg. 651: 1 – 95 eoo (137-144) and from your Foerster text pg. 762: problems 14, 15, 17, 18, 19, 21, 22
Thursday, 5-9: Quiz and Review: Pg. 651: 1 – 95 eoo, (137-144) and from your Foerster text pg. 762: problems 14, 15, 17, 18, 19, 21, 22
I assigned problem # 19 from your text was because it involved an investigation of the Golden Ratio (phi). The reason I want you to do this is because several of you have asked how to find the explicit form of the Fibonacci sequence. Well here is a pretty decent explanation of that, but until you realize that the ratio of successive terms of the Fibonacci sequence converge to phi, you don't know why they assume that the Fibonacci sequence is related to a geometric one.
Friday, 5-10 Sequence Review
Monday, 5-13 Test on Sequences/Sequence lab due
MAKE SURE YOU HAVE DATA FOR BOTH LABS DUE THIS WEEK!!
I CAN'T TAKE MAKE-UP WORK AFTER FRIDAY!
Tuesday, 5-14: Review/Parametric and Vector labs due for 1st period
Here is the parametric activity we did today.
Wednesday, 5-15 Review/Vector lab due for 2nd period
Here are review sheets made by Emily last year. Thank her for these!
Trig Identities Trig Applications 2D Vectors Parametrics Polar 3D Vectors Sequences
Her final exam review is on my blog, but here are more problems to work. They aren't too challenging, but they may help
you remember important concepts.
Thursday, 5-16 Review/Parametric lab due for 2nd period
Friday, 5-17 Retest Opportunity - LAST DAY FOR MAKE-UP WORK!
Monday, 5-20 FINAL EXAM
Friday, 4/13: We took a quiz Wednesday, got an Interesting Sequence to investigate,and looked at Mathematical Induction on Thursday. Today the Interesting Sequence tasks were due and the assignment this weekend is to complete an investigation of the Golden Ratio (phi). The reason I want you to do this is because several of you have asked how to find the explicit form of the Fibonacci sequence. Well here is a pretty decent explanation of that, but until you realize that the ratio of successive terms of the Fibonacci sequence converge to phi, you don't know why they assume that the Fibonacci sequence is related to a geometric one.