Find the 31st term of the following sequence. 9, 15, 21, ...
1 answer:
Notice that the above sequence is arithmetic because the common difference: d is constant.
d = second term - first term.
= 15 - 9
= 6
The general term of an arithmetic sequence is,
a_{n} =a_{1} +(n-1)d
Where , nth term =
= First term
and d = common difference.
The given sequence is: 9, 15, 21, ...
Here a_{1} = 9,
d = 6
We need to find the 31st term. So, n = 31.
Next step is to plug in these values in the above formula. Therefore,
= 9 + 30* 6
= 9 + 180
= 189
So, 31st term of this sequence is 189.
Hope this helps you.
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Step-by-step explanation:
Collect like terms and simplify
[tex] -10n+30n=-36-24 \\ 20n = -60 [/tex]
Divide both sides of the equation by 20
[tex] 20n/20 = -60/20 \\ n=-3 [/tex]
Answer:
<h2>Y=1/2x-1</h2>Find where the expression
1/2x−1 is undefined.
x=1/2
Consider the rational function
R(x)=ax^n/bx^m where n is the degree of the numerator and m is the degree of the denominator.
1. If n<m, then the x-axis, y=0, is the horizontal asymptote.
2. If n=m, then the horizontal asymptote is the line y = ab.
3. If n>m, then there is no horizontal asymptote (there is an oblique asymptote).
Find n and m.n=0m=1
Since n<m, the x-axis, y=0, is the horizontal asymptote.y=0
There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.
No Oblique Asymptotes
This is the set of all asymptotes.
Vertical Asymptotes:
x=1/2
Horizontal Asymptotes:
y=0
No Oblique Asymptotes
<h2>2x+y=4</h2>Subtract 2x from both sides of the equation.
y=4−2x
Rewrite in slope-intercept form.
The slope-intercept form is
y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Reorder 4 and −2x.
y=−2x+4
Use the slope-intercept form to find the slope and y-intercept.
Find the values of m and b using the form
y=mx+b.
m= - 2b=4
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: −2
y-intercept: (0,4)
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y
values.
Find the x-intercept.
x-intercept(s):
(2,0)
Find the y-intercept.
y-intercept(s):
(0,4)
Create a table of the x and y values.
x y
0 4
2 0
Graph the line using the slope and the y-intercept, or the points.
Slope: −2
y-intercept:
(0,4)
Step-by-step explanation:
Hope it is helpful...
