Response: For question 38, they are asking you to write a sequence to show the relationship between the number of points and the number of lines connecting the points. n represents the number of dots and tn represents the number of lines. So:
For n=1, there are no lines, tn = 0
For n=2, there is 1 line, tn = 1
For n=3, there are 3 lines, tn=3
And so forth. Write your values of tn in a sequence as so: {0, 1, 3, …tn}
In question 39, n represents the number of sides (the lines around the outside) and the sequence is the number of diagonals that cut through the middle of your shape.
So,
n= 3 is the triangle with tn= 0 (there are no lines cutting through the middle)
n=4 is the next shape (square) with tn=2 (there are two lines that criss cross)
n= 5 has tn=5
and so forth.
Question: On question 41, I am confused because I do not understand how to begin the question. Is the first term T0? As in T0, T0.2, T0.4? If so, is N the height in metres or the seconds?
Response: For Question 41, the terms tn are in the {} brackets. n= 0, 0.2, 0.4, 0.6, 0.8 and 1. n represents the number of seconds that has passed since the frisbee was thrown. The terms are tn ={2.00, 3.12, ….6.00}. These terms represent the height of the frisbee from the ground.
Question: What are we suppose to do for the last page of the Power Sequences homework?
Response: The last page of the homework asks you to analyze the sequence and provide information on them.
For example, with #2, the sequence is {-1, -6, -15, -28, -45, -66…}
– what are the next 2 terms? To figure this out, you will need to figure out what kind of function would produce this. What is the D1 difference? What is the D2 difference? Where is there a common difference? If this is a linear sequence, you would find your common difference in D1. If it is a quadratic sequence, you would find your common difference in D2, etc.
– once you have figured out what type of sequence you have, you can work backwards from the D1 or D2 common differences to figure out what the next two terms are. This will require you to do some problem solving. If the common difference is 4 in D1, what would your next term be? If your common difference is something in D2, you need to figure out what the difference in terms would be in D1 before you can apply it to the sequence.
– Power? This question basically asks if this is a type of function you’ve seen before. If there are no common differences, then it is not a power function.
– Level of common difference? That is just asking if your common difference is in D1, D2, etc.
– Common Difference? That is asking what the difference actually is
Going back to #2:
My D1 is equal to: {-6-(-1), -15-(-6), -28-(-15)…}
My D2 is equal to: {-4, -4, -4, -4…}
So my common difference is -4 and it is at the second level. It is a power sequence. It is a quadratic sequence because the common difference is at D2.
To figure out the next two terms, I need to look at the last two terms given and the common difference. The D1 difference between -45 and -66 is -21. I know that the D2 difference is -4, which tells me that each term in D1 is -4 of the one before it. So, the next D1 difference would be -25 and then -29. Knowing the next two D1 differences, I can just subtract -25 from the last term in the sequence (-66-25=-91) and thn -29 from -91 (-120).
So, the sequence is {-1, -6, -15, -28, -45, -66, -91, -120}
Blogarithmic Growth 