Question

# Write a recursive formula for the given sequence. 47, 39, 31, 23, 15, ....

Hint:

- Recursive Formula is a formula that defines the each term of sequence using the previous/preceding terms.

## The correct answer is: a_n=a_(n-1)-8.

### Explanation:

- We have given a sequence 47,39,31,23,15,...
- We have to find the recursive formula.

Step 1 of 1:

We have given a sequence 47, 39, 31, 23, 15, ....

The given sequence is an AP.

We know that the recursive formula for any AP is , where d is common difference.

Here the common difference is - 8

So, The recursive formula is

### Related Questions to study

### Write a recursive formula for the given sequence. 81,85,89,93,97,....

**Explanation:**

We have given a sequence 81,85,89,93,97,...

The given sequence is an AP.

We know that the recursive formula for any AP is , where d is common difference.

Here the common difference is 4

So, The recursive formula is

- We have given a sequence 81,85,89,93,97,...
- We have to find the recursive formula.

We have given a sequence 81,85,89,93,97,...

The given sequence is an AP.

We know that the recursive formula for any AP is , where d is common difference.

Here the common difference is 4

So, The recursive formula is

**Write a recursive formula for the given sequence. 81,85,89,93,97,....**

**Maths-General**

**Explanation:**

We have given a sequence 81,85,89,93,97,...

The given sequence is an AP.

We know that the recursive formula for any AP is , where d is common difference.

Here the common difference is 4

So, The recursive formula is

- We have given a sequence 81,85,89,93,97,...
- We have to find the recursive formula.

We have given a sequence 81,85,89,93,97,...

The given sequence is an AP.

We know that the recursive formula for any AP is , where d is common difference.

Here the common difference is 4

So, The recursive formula is

**Maths-Explanation:**

We have given sequence 4,7,10,14,...

The difference in first two terms is

Now the difference in next two terms is

Then, The difference between next two terms will be

Since the difference is not constant

The given sequence is not an arithmetic sequence.Maths-GeneralExplanation:

We have given sequence 4,7,10,14,...

The difference in first two terms is

Now the difference in next two terms is

Then, The difference between next two terms will be

Since the difference is not constant

The given sequence is not an arithmetic sequence.Maths-### How do you find vertical and horizontal asymptotes of a rational function?

x

x

x(x + 3) + 4 (x + 3) = 0

(x + 3)(x + 4)=0

x= -3 or x = -4

The vertical asymptote of the rational function is x=−3 and x=-4

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= -3 and x = -4.### How do you find vertical and horizontal asymptotes of a rational function?

Maths-General

x

x

x(x + 3) + 4 (x + 3) = 0

(x + 3)(x + 4)=0

x= -3 or x = -4

The vertical asymptote of the rational function is x=−3 and x=-4

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= -3 and x = -4.Maths-

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

The difference in first two terms is

Now the difference in next two terms is

Maths-General

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

The difference in first two terms is

Now the difference in next two terms is

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

We have given a explicit formula a

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

Maths-General

We have given a explicit formula a

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

We have given a explicit formula a

Now,

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

Maths-General

We have given a explicit formula a

Now,

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

1.Find the asymptotes of the rational function, if any.

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.

Maths-General1.Find the asymptotes of the rational function, if any.

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) = =1Maths-### Write an explicit formula for the arithmetic sequence.

We know that the common difference d is also equal to

Now in given question we have

Ie,

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

Maths-General

We know that the common difference d is also equal to

Now in given question we have

Ie,

Maths-

We know that the common difference d is also equal to

Now in given question we have

Ie,

Maths-General

We know that the common difference d is also equal to

Now in given question we have

Ie,

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

1.Find the asymptotes of the rational function, if any.

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.

Maths-General1.Find the asymptotes of the rational function, if any.

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) = =3Maths-

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

Here

Maths-General

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

Here

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

We have given the equation of the daily attendance at an amusement park after day x

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

Maths-GeneralWe have given the equation of the daily attendance at an amusement park after day x

F(x) =

We have to find on which day attendance will be 1125

y = f(x) = 1125

x = -1.001 or x= 0.999

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

4x

4x

x

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

Maths-General

4x

4x

x

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.Maths-### Graph each function and identify the horizontal and vertical asymptotes

x

x

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

Maths-General

x

x

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.Maths-

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,

Maths-General

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,

### Write a recursive formula for the given sequence. 81,85,89,93,97,....

- We have given a sequence 4,7,10,14,..
- We have to find weather the given sequence is AP or not.

We have given sequence 4,7,10,14,...

The difference in first two terms is

Now the difference in next two terms is

Then, The difference between next two terms will be

Since the difference is not constant

The given sequence is not an arithmetic sequence.

### Write a recursive formula for the given sequence. 81,85,89,93,97,....

- We have given a sequence 4,7,10,14,..
- We have to find weather the given sequence is AP or not.

We have given sequence 4,7,10,14,...

The difference in first two terms is

Now the difference in next two terms is

Then, The difference between next two terms will be

Since the difference is not constant

The given sequence is not an arithmetic sequence.

### How do you find vertical and horizontal asymptotes of a rational function?

What are the vertical asymptotes for the graph of

- 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}+7x + 12 = 0

x

^{2}+ 3x + 4x + 12 = 0

x(x + 3) + 4 (x + 3) = 0

(x + 3)(x + 4)=0

x= -3 or x = -4

The vertical asymptote of the rational function is x=−3 and x=-4

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= -3 and x = -4.

### How do you find vertical and horizontal asymptotes of a rational function?

What are the vertical asymptotes for the graph of

- 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}+7x + 12 = 0

x

^{2}+ 3x + 4x + 12 = 0

x(x + 3) + 4 (x + 3) = 0

(x + 3)(x + 4)=0

x= -3 or x = -4

The vertical asymptote of the rational function is x=−3 and x=-4

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= -3 and x = -4.

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

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

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.

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

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

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.

### 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 .

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 .

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

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