Write the frost ten terms of a sequence whose first term is -10 and whose common difference is -2
1 answer:
Answer:
Step-by-step explanation:
we know that
In an <u><em>Arithmetic Sequence</em></u> the difference between one term and the next is a constant, called the common difference
The formula for an Arithmetic Sequence is equal to
where
d is the common difference
n is the number of terms
a_1 is the first term of the sequence
In this problem we have
substitute
so
<u><em>Find the first ten terms</em></u>
For n=2 ---->
For n=3 ---->
For n=4 ---->
For n=5 ---->
For n=6 ---->
For n=7 ---->
For n=8 ---->
For n=9 ---->
For n=10 ---->
The sequence is
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The closest point on a line, to another point, will be a point that's on a normal of that line, or a line that is perpendicular to it, notice picture below
so, y = 2x, has a slope of 2, a perpendicular line to it, will have a slope of negative reciprocal that, or
so, we know that line passes through the point 20,0, and has a slope of -1/2
if we plug that in the point-slope form, we get
now, the point that's on 2x and is also on that perpendicular line, is the closest to 20,0 from 2x, thus, is where both graphs intersect, as you can see in the graph
thus
solve for "x'
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not sure on the 2nd part, but sounds like, what's the distance from that point to 20,0, well, if that's the case, just use the distance equation
so, y = 2x, has a slope of 2, a perpendicular line to it, will have a slope of negative reciprocal that, or
so, we know that line passes through the point 20,0, and has a slope of -1/2
if we plug that in the point-slope form, we get
now, the point that's on 2x and is also on that perpendicular line, is the closest to 20,0 from 2x, thus, is where both graphs intersect, as you can see in the graph
thus
------------------------------------------------------------
not sure on the 2nd part, but sounds like, what's the distance from that point to 20,0, well, if that's the case, just use the distance equation
Answer:
12.123
Step-by-step explanation:
You want the area under the curve f(x) = √(3x+5) on the interval [0, 4] estimated using the left sum and four subintervals.
<h3>Riemann sum</h3>When the interval [0, 4] is divided into four equal parts, each has unit width. That means the area of the rectangle defined by the curve and the interval width will be equal to the value of the curve at the left end of the interval.
The area we want is the sum ...
f(0) +f(1) +f(2) +f(3)
As the attachment shows, that sum is ...
area ≈ 12.123 . . . square units
__
<em>Additional comment</em>
The table values in the attachment are rounded to 7 decimal places. Trailing zeros are not shown. Actual values used have 12 significant digits, as the total shows.
Such a sum is called a Riemann sum, named for a German mathematician. Four such sums are commonly used, and further refinements are possible. Those are the left sum (as here), the right sum, the midpoint sum, and a sum using a trapezoidal approximation of the rectangle area.
For left, right, and midpoint sums, n function values are required for n subintervals. When the trapezoidal approximation is used, n+1 function values are required.
