So, I just found out I can post questions here instead of emailing the instructor, I have looked through previous posts, but wasn't still quite sure about these.
[Series of Question 1 - From Guide #1]
P. 106 - 8 Sequence
P. 117 - 7 SQRT(2)/2 = 1 ??? Is this an error??
I have posted more for different books.
Thanks.
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- sendalot
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Re: Series of Question 1 - From Guide #1
Hi!
Two great questions here. Here's the statement of the problem for the first:
Guide 1, page 107, #8 (at the bottom of the page)
8. If each number of a sequence is 4 more than the previous number, and the 3rd number in the sequence is 13, what is the 114th number in the sequence?
There is a good explanation of a similar problem right above it on the page, which we can apply to this problem directly. Instead of finding a rule for the sequence, we can consider this reasoning:
Between the 3rd and 114th terms of the sequence, there are 111 "jumps" of size 4. Since 4x111 = 444, there is an increase of 444 between the 3rd and 114th terms. Then the 114th term is 13 + 444 = 457.
If you want to find a rule for the sequence, the first thing we need to do is translate this word problem into algebra. The problem says we're dealing with a sequence, so let's call the terms of that sequence S_n
"If each number of a sequence is 4 more than the previous number..." This is an example of an arithmetic sequence, because there is a constant difference of 4 between consecutive terms. Arithmetic sequences have a special form which we can use here: S_n = S_1 + (n-1)*d.
We're given the constant difference (d = 4), so to find out swhat S_114 is, we'll need to find S_1. We can find S_1 by solving the equation S_n = S_1 + (n-1)*d when n = 3, because we know S_3 = 13.
S_1 + (3-1)*4 = S_3 = 13
S_1 + 8 = 13
S_1 = 5
Now we can plug this back in to our recurrence when n = 114.
S_114 = S_1 + (114 - 1) * 4
S_114 = 5 + 113 * 4
S_114 = 5 + 452
S_114 = 457, just like we expected.
Okay, on to the next one:
Book 1, Page 117 #7
You are correct--there is a typo in this answer. It currently reads: c = rad(W/L) [...] If the original value of W is 2 and the original value of L is 2, the original value of c is rad(2)/2 = 1.
Of course, rad(2)/2 is not equal to 1--good catch. It should read "...the original value of c is rad(2/2) = 1."
Great work!
Michael
Two great questions here. Here's the statement of the problem for the first:
Guide 1, page 107, #8 (at the bottom of the page)
8. If each number of a sequence is 4 more than the previous number, and the 3rd number in the sequence is 13, what is the 114th number in the sequence?
There is a good explanation of a similar problem right above it on the page, which we can apply to this problem directly. Instead of finding a rule for the sequence, we can consider this reasoning:
Between the 3rd and 114th terms of the sequence, there are 111 "jumps" of size 4. Since 4x111 = 444, there is an increase of 444 between the 3rd and 114th terms. Then the 114th term is 13 + 444 = 457.
If you want to find a rule for the sequence, the first thing we need to do is translate this word problem into algebra. The problem says we're dealing with a sequence, so let's call the terms of that sequence S_n
"If each number of a sequence is 4 more than the previous number..." This is an example of an arithmetic sequence, because there is a constant difference of 4 between consecutive terms. Arithmetic sequences have a special form which we can use here: S_n = S_1 + (n-1)*d.
We're given the constant difference (d = 4), so to find out swhat S_114 is, we'll need to find S_1. We can find S_1 by solving the equation S_n = S_1 + (n-1)*d when n = 3, because we know S_3 = 13.
S_1 + (3-1)*4 = S_3 = 13
S_1 + 8 = 13
S_1 = 5
Now we can plug this back in to our recurrence when n = 114.
S_114 = S_1 + (114 - 1) * 4
S_114 = 5 + 113 * 4
S_114 = 5 + 452
S_114 = 457, just like we expected.
Okay, on to the next one:
Book 1, Page 117 #7
You are correct--there is a typo in this answer. It currently reads: c = rad(W/L) [...] If the original value of W is 2 and the original value of L is 2, the original value of c is rad(2)/2 = 1.
Of course, rad(2)/2 is not equal to 1--good catch. It should read "...the original value of c is rad(2/2) = 1."
Great work!
Michael
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