Question

# Write recursive formula and find the first term.

Hint:

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

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

### Explanation:

- We have given a explicit function .
- We have to find the recursive formula and first term.

Step 1 of 2:

We have given explicit formula .

First term will be

Step 2 of 2:

Now for recursive formula we will calculate a_{n-1.}

So,

.

Step 2 of 2:

Now for recursive formula we will calculate a

_{n-1.}

So,

.

### Related Questions to study

### Are graphs of the equations parallel, perpendicular or neither?

- We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.

We have given two equations

y = 4x + 1

y = -4x - 2

Slope of both lines are 4, -4 respectively

Since slope are not equal then both are not parallel.

Product of both slope is 4 × -4 = -16

So, both are not perpendicular also.

So,

Both are nor parallel neither perpendicular.

### Are graphs of the equations parallel, perpendicular or neither?

- We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.

We have given two equations

y = 4x + 1

y = -4x - 2

Slope of both lines are 4, -4 respectively

Since slope are not equal then both are not parallel.

Product of both slope is 4 × -4 = -16

So, both are not perpendicular also.

So,

Both are nor parallel neither perpendicular.

### Write recursive formula and find the first term.

- We have given a explicit function .
- We have to find the recursive formula and first term.

We have given explicit formula .

First term will be

Step 2 of 2:

Now for recursive formula we will calculate .

So,

.

### Write recursive formula and find the first term.

- We have given a explicit function .
- We have to find the recursive formula and first term.

We have given explicit formula .

First term will be

Step 2 of 2:

Now for recursive formula we will calculate .

So,

.

### Are graphs of the equations parallel, perpendicular or neither?

- We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.

We have given two equations

x - 3y = 6

x - 3y = 9

Slope of both lines are respectively

Since slope are equal then both are parallel.

### Are graphs of the equations parallel, perpendicular or neither?

We have given two equations

x - 3y = 6

x - 3y = 9

Slope of both lines are respectively

Since slope are equal then both are parallel.

### What is 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}+ 2x - 15= 0

x

^{2}+ 5x -3x - 15= 0

x(x + 5) - 3 (x + 5) = 0

(x – 3) (x + 5) = 0

x – 3 = 0 or x + 5 = 0

x = 3 or x = -5

The vertical asymptote of the rational function is x = 3 and x = -5 .

This function has the x - intercept at (1.667,0) and y -intercept at (0,1) . We will find more points on the function and graph the function.

### What is 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}+ 2x - 15= 0

x

^{2}+ 5x -3x - 15= 0

x(x + 5) - 3 (x + 5) = 0

(x – 3) (x + 5) = 0

x – 3 = 0 or x + 5 = 0

x = 3 or x = -5

The vertical asymptote of the rational function is x = 3 and x = -5 .

This function has the x - intercept at (1.667,0) and y -intercept at (0,1) . We will find more points on the function and graph the function.

### Find the equation for a path that passes through the point (-4, 9) and is parallel to .

- We have been given an equation that represents y-axis.
- We have to find an equation for a path that passes through the point (-4,9) and is perpendicular to

We have given a line passes through a point (-4, 9) 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

### Find the equation for a path that passes through the point (-4, 9) and is parallel to .

- We have been given an equation that represents y-axis.
- We have to find an equation for a path that passes through the point (-4,9) and is perpendicular to

We have given a line passes through a point (-4, 9) 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 explicit formula.

- We have given
- We have to find the explicit formula of the given sequence.

We know that the recursive formula of an AP is , where d is common difference.

Here we have

So, d = -7

Also, We have a

_{1}= -3

So, The explicit formula will be

.

### Write explicit formula.

- We have given
- We have to find the explicit formula of the given sequence.

We know that the recursive formula of an AP is , where d is common difference.

Here we have

So, d = -7

Also, We have a

_{1}= -3

So, The explicit formula will be

.

### Write explicit formula.

- We have given
- We have to find the explicit formula of the given sequence.

We know that the recursive formula of an AP is , where d is common difference.

Here we have

So, d = 1

Also, We have a

_{1}= 12

So, The explicit formula will be

### Write explicit formula.

- We have given
- We have to find the explicit formula of the given sequence.

We know that the recursive formula of an AP is , where d is common difference.

Here we have

So, d = 1

Also, We have a

_{1}= 12

So, The explicit formula will be

### Write explicit formula.

- We have given
- We have to find the explicit formula of the given sequence.

We know that the recursive formula of an AP is , where d is common difference.

Here we have

So, d = -21

Also, We have a

_{1}= 56

So, The explicit formula will be

### Write explicit formula.

- We have given
- We have to find the explicit formula of the given sequence.

We know that the recursive formula of an AP is , where d is common difference.

Here we have

So, d = -21

Also, We have a

_{1}= 56

So, The explicit formula will be

### Graph each function

Solution:-

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 - 1= 0

x = 1

The vertical asymptote of the rational function is x= 1

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 horizontal asymptote is

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

### Graph each function

Solution:-

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 - 1= 0

x = 1

The vertical asymptote of the rational function is x= 1

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 horizontal asymptote is

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

### Find the equation for a path that passes through the point (6, 6) and is perpendicular to .

- We have been given an equation that represents y-axis.
- We have to find an equation for a path that passes through the point (6, 6) and is perpendicular to

We have given a line passes through a point (6, 6) and perpendicular to a line

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

So,

Therefore the equation of the line will be

### Find the equation for a path that passes through the point (6, 6) and is perpendicular to .

- We have been given an equation that represents y-axis.
- We have to find an equation for a path that passes through the point (6, 6) and is perpendicular to

We have given a line passes through a point (6, 6) and perpendicular to a line

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

So,

Therefore the equation of the line will be

### Write explicit formula.

- We have given
- We have to find the explicit formula of the given sequence.

We know that the recursive formula of an AP is , where d is common difference.

Here we have

So, d = -2

Also, We have

So, The explicit formula will be

### Write explicit formula.

- We have given
- We have to find the explicit formula of the given sequence.

We know that the recursive formula of an AP is , where d is common difference.

Here we have

So, d = -2

Also, We have

So, The explicit formula will be

### Write explicit formula.

- We have given
- We have to find the explicit formula of the given sequence.

We know that the recursive formula of an AP is , where d is common difference.

Here we have

So, d = 6

Also, We have a

_{1}= 9

So, The explicit formula will be

### Write explicit formula.

- We have given
- We have to find the explicit formula of the given sequence.

We know that the recursive formula of an AP is , where d is common difference.

Here we have

So, d = 6

Also, We have a

_{1}= 9

So, The explicit formula will be

### Write explicit formula.

- We have given
- We have to find the explicit formula of the given sequence.

We know that the recursive formula of an AP is , where d is common difference.

Here we have

So, d = 15

Also, We have a

_{1}= 8

So, The explicit formula will be

### Write explicit formula.

- We have given
- We have to find the explicit formula of the given sequence.

We know that the recursive formula of an AP is , where d is common difference.

Here we have

So, d = 15

Also, We have a

_{1}= 8

So, The explicit formula will be

### Graph each function

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 + 8= 0

x = -8

The vertical asymptote of the rational function is x=-8

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= -8 and horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) = = 4

### Graph each function

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 + 8= 0

x = -8

The vertical asymptote of the rational function is x=-8

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= -8 and horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) = = 4

### What is the graph of the function

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 .

3x - 4= 0

3x = 4

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) =

### What is the graph of the function

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 .

3x - 4= 0

3x = 4

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) =