NO LINKS!!!!
1 answer:
9514 1404 393
Answer:
a. 12, 16, 20, 24; t(n)=4n
b. 16, 32, 64, 128; t(n)=2·2^n
Step-by-step explanation:
a. The difference of the given terms is 8-4=4, so the arithmetic sequence has a first term of 4 and a common difference of 4. The general term has the formula ...
t(n) = t(1) +d(n -1)
t(n) = 4 +4(n -1) . . . . . with t(1) and d filled in
t(n) = 4n . . . . . . . . . . simplified
This formula can be considered to be the generator of the sequence. For values of n from 3 to 6, the next four terms are ...
t(3) = 12; t(4) =16; t(5) = 20, t(6) = 24
A table and graph are shown in the first attachment.
__
b. The ratio of the given terms is 8/4 = 2, so the geometric sequence has a first term of 4 and a common ratio of 2. The general term has the formula ...
t(n) = t(1)·r^(n-1)
t(n) = 4·2^(n-1) . . . . . . . with t(1) and r filled in
t(n) = 2·2^n . . . . . . . . simplified
This formula can be considered to be the generator of the sequence. For values of n from 3 to 6, the next four terms are ...
t(3) = 16; t(4) = 32; t(5) = 64; t(6) = 128
A table and graph are shown in the second attachment.
You might be interested in
<h3>Answer: Choice B</h3><h3>{4,5,6,7}</h3>
====================================================
Explanation:
Set A = {4,5,6,7,8,9} since these values are larger than 3 and smaller than 10. We only consider whole numbers in this range.
Set B = {1,2,3,4,5,6,7} represents positive whole numbers less than 8
To find the set we need to see which values are in both A and B at the same time. Those values are {4,5,6,7}
So
--------
side note: the notation means "A intersect B", so we're looking at where the two sets intersect or overlap (ie what they have in common).
Answer and Step-by-step explanation:
1) If you graph the lines, you will get the lines in the first attachment. You will see that the intersection point is (3, 5), which is the solution to that system.
2) First, let's convert both of these into slope-intercept form so that they're easier to graph.
x - 3y = 2
x = 3y + 2
3y = x - 2
y =
AND
-3x + 9y = -6
9y = 3x - 6
y =
We see that these two lines are exactly the same, which means that no matter what coordinate works for one, it will work for the other. In other words, there are infinitely many solutions.
And, if you graph these lines, you will get the graph in the second attachment, where they are the same line.
Hope this helps!
