Question

# Tell whether the given sequence is an arithmetic sequence. 15,13,11,9,....

Hint:

- A sequence is said to be arithmetic if the common difference is always constant.
- The General formula of any AP is .

## The correct answer is: ⇒-2

### Explanation:

- We have given a sequence 15,13,11,9,...
- We have to find weather the given sequence is AP or not.

Step 1 of 1:

We have given sequence 15,13,11,9,...

The difference in first two terms is

Now the difference in next two terms is

Since the difference is constant

The given sequence is arithmetic sequence.

Now the difference in next two terms is

Since the difference is constant

The given sequence is arithmetic sequence.

### Related Questions to study

### Write an explicit formula for the arithmetic sequence.

a_{n} = 12 - 5n

- We have given an explicit formula a
_{n}= 12 - 5n - We have to find the recursive formula

We have given a explicit formula a

_{n}= 12 - 5n

Now,

So, The recursive formula is .

### Write an explicit formula for the arithmetic sequence.

a_{n} = 12 - 5n

- We have given an explicit formula a
_{n}= 12 - 5n - We have to find the recursive formula

We have given a explicit formula a

_{n}= 12 - 5n

Now,

So, The recursive formula is .

### Write an explicit formula for the arithmetic sequence.

a_{n} = 8 + 3n

- We have given an explicit formula a
_{n}= 8 + 3n - We have to find the recursive formula

We have given a explicit formula a

_{n}= 8 + 3n

Now,

So, The recursive formula is .

### Write an explicit formula for the arithmetic sequence.

a_{n} = 8 + 3n

- We have given an explicit formula a
_{n}= 8 + 3n - We have to find the recursive formula

We have given a explicit formula a

_{n}= 8 + 3n

Now,

So, The recursive formula is .

### Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.

2.Draw the asymptotes as dotted lines.

3.Find the x -intercept (s) and y -intercept of the rational function, if any.

4.Find the values of y for several different values of x .

5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.

The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

x - 6= 0

x = 6

The vertical asymptote of the rational function is x= 6

We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x= 6 and horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) = =1

### Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.

2.Draw the asymptotes as dotted lines.

3.Find the x -intercept (s) and y -intercept of the rational function, if any.

4.Find the values of y for several different values of x .

5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.

The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

x - 6= 0

x = 6

The vertical asymptote of the rational function is x= 6

We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x= 6 and horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) = =1

### Write an explicit formula for the arithmetic sequence.

- We have given and
- We have to find the explicit formula for this AP.

We know that the common difference d is also equal to

Now in given question we have

Ie,

And a_{1} = -1

So, The explicit formula will be

### Write an explicit formula for the arithmetic sequence.

- We have given and
- We have to find the explicit formula for this AP.

We know that the common difference d is also equal to

Now in given question we have

Ie,

And a_{1} = -1

So, The explicit formula will be

### Write an explicit formula for the arithmetic sequence.

- We have given a
_{n}= a_{n - 1}- 3 and a_{1}= 10 - We have to find the explicit formula for this AP.

We know that the common difference d is also equal to

Now in given question we have

Ie,

And a_{1} = 10

So, The explicit formula will be

### Write an explicit formula for the arithmetic sequence.

- We have given a
_{n}= a_{n - 1}- 3 and a_{1}= 10 - We have to find the explicit formula for this AP.

We know that the common difference d is also equal to

Now in given question we have

Ie,

And a_{1} = 10

So, The explicit formula will be

### Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.

2.Draw the asymptotes as dotted lines.

3.Find the x -intercept (s) and y -intercept of the rational function, if any.

4.Find the values of y for several different values of x .

5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.

The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

2x + 1= 0

x =

The vertical asymptote of the rational function is x =

We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x= and horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) = =3

### Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.

2.Draw the asymptotes as dotted lines.

3.Find the x -intercept (s) and y -intercept of the rational function, if any.

4.Find the values of y for several different values of x .

5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.

The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

2x + 1= 0

x =

The vertical asymptote of the rational function is x =

We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x= and horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) = =3

### The cost to rent a bike is 28 for the first day plus 2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting a bike for 8 days?

- We have given a cost of rent of bike 28 for the first day plus2 for each day after that.
- We have to write an explicit formula for the rental cost for n days and cost of renting bike for 8 days.

We have given first day cost is 28 and for each more day 2 will be charged

Here

a_{1} = 28

d = 2

We know that general formula is a_{n} = a_{1} + (n - 1)d

So,

Step 2 of 2:

Now, Cost of renting for 8 days will be

### The cost to rent a bike is 28 for the first day plus 2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting a bike for 8 days?

- We have given a cost of rent of bike 28 for the first day plus2 for each day after that.
- We have to write an explicit formula for the rental cost for n days and cost of renting bike for 8 days.

We have given first day cost is 28 and for each more day 2 will be charged

Here

a_{1} = 28

d = 2

We know that general formula is a_{n} = a_{1} + (n - 1)d

So,

Step 2 of 2:

Now, Cost of renting for 8 days will be

### The daily attendance at an amusement park after day x is given by the function

f(x) =. On Approximately which day will the attendance be 1125 people ?

F(x) =

We have to find on which day attendance will be 1125

y = f(x) = 1125

x = -1.001 or x= 0.999

### The daily attendance at an amusement park after day x is given by the function

f(x) =. On Approximately which day will the attendance be 1125 people ?

F(x) =

We have to find on which day attendance will be 1125

y = f(x) = 1125

x = -1.001 or x= 0.999

### Graph each function and identify the horizontal and vertical asymptotes

- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .
- Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.

4x

^{2}-25 = 0

4x

^{2}= 25

x

^{2}=

x = and x =

The vertical asymptote of the rational function is x=−1.

This function has no x -intercept at (4,0) and y -intercept at (0,7) . We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x= and horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) = = 0.75.

### Graph each function and identify the horizontal and vertical asymptotes

- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .
- Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.

4x

^{2}-25 = 0

4x

^{2}= 25

x

^{2}=

x = and x =

The vertical asymptote of the rational function is x=−1.

This function has no x -intercept at (4,0) and y -intercept at (0,7) . We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x= and horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) = = 0.75.

### Graph each function and identify the horizontal and vertical asymptotes

- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .
- Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.

x

^{2}+ 2x + 1= 0

x

^{2}+x + x + 1= 0

x(x + 1) + 1 (x + 1) = 0

(x + 1) (x + 1) = 0

x + 1 = 0 or x + 1 = 0

x = -1

The vertical asymptote of the rational function is x=−1.

This function has no x -intercept and y -intercept at (0,7) . We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x = -1 and degree of the numerator is greater than the denominator, then there is no horizontal asymptote.

### Graph each function and identify the horizontal and vertical asymptotes

- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .

x

^{2}+ 2x + 1= 0

x

^{2}+x + x + 1= 0

x(x + 1) + 1 (x + 1) = 0

(x + 1) (x + 1) = 0

x + 1 = 0 or x + 1 = 0

x = -1

The vertical asymptote of the rational function is x=−1.

This function has no x -intercept and y -intercept at (0,7) . We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x = -1 and degree of the numerator is greater than the denominator, then there is no horizontal asymptote.

### Write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of y = 2x + 3

- We have to write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of 𝑦 = 2𝑥 + 3.

We have to find a line passes through a point (4, 5) and perpendicular to a line 𝑦 = 2𝑥 + 3.

Since product of two perpendicular lines is equal to -1.

So,

Therefore the equation of the line will be

### Write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of y = 2x + 3

- We have to write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of 𝑦 = 2𝑥 + 3.

We have to find a line passes through a point (4, 5) and perpendicular to a line 𝑦 = 2𝑥 + 3.

Since product of two perpendicular lines is equal to -1.

So,

Therefore the equation of the line will be

### Graph each function and identify the horizontal and vertical asymptotes

- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .

x – 2 = 0

x = 2

The vertical asymptote of the rational function is x= 2.

This function has no x -intercept and has y -intercept at (0,-1.5) . We will find more points on the function and graph the function

From the graph we can analyze that the vertical asymptote of the rational function is x= 2 and horizontal asymptote is y = 0

### Graph each function and identify the horizontal and vertical asymptotes

- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .

x – 2 = 0

x = 2

The vertical asymptote of the rational function is x= 2.

This function has no x -intercept and has y -intercept at (0,-1.5) . We will find more points on the function and graph the function

From the graph we can analyze that the vertical asymptote of the rational function is x= 2 and horizontal asymptote is y = 0

### Graph each function and identify the horizontal and vertical asymptotes

- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .

x

^{2}- 1= 0

x = 1 or x = -1

The vertical asymptote of the rational function is x=−1 and x= 1 .

This function has the x -intercept at (−14,0) and y -intercept at (0,4.167) . We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x =−1 and x = 1 and horizontal asymptote is y = 0

### Graph each function and identify the horizontal and vertical asymptotes

- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .

x

^{2}- 1= 0

x = 1 or x = -1

The vertical asymptote of the rational function is x=−1 and x= 1 .

This function has the x -intercept at (−14,0) and y -intercept at (0,4.167) . We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x =−1 and x = 1 and horizontal asymptote is y = 0

### Write an equation of the line in slope-intercept form that passes through the point (-3, 5) and is parallel to .

- We have been given in the question two points for which we have to write an equation of the line in slope-intercept form that passes through the point (-3, 5) and is parallel to

We have to find a line passes through a point (-3, 5) and parallel to a line

Since two parallel lines have same slope.

So, Slope of the line will be

Therefore the equation of the line will be

.

### Write an equation of the line in slope-intercept form that passes through the point (-3, 5) and is parallel to .

- We have been given in the question two points for which we have to write an equation of the line in slope-intercept form that passes through the point (-3, 5) and is parallel to

We have to find a line passes through a point (-3, 5) and parallel to a line

Since two parallel lines have same slope.

So, Slope of the line will be

Therefore the equation of the line will be

.