Question

# Write explicit formula.

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: a_n=77-21n

### Explanation:

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

Step 1 of 1:

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

### Related Questions to study

### 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) =

### Write recursive formula and explicit formula. -15,-6,-3,12,21,...

- We have given a sequence -15,-6,-3,12,21,.....
- We have to find the recursive and explicit formula of the given sequence.

We have given a sequence -15,-6,-3,12,21,.....

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 9

So, The recursive formula is

Step 2 of 2:

The given sequence is an AP.

So, The explicit formula will be

### Write recursive formula and explicit formula. -15,-6,-3,12,21,...

- We have given a sequence -15,-6,-3,12,21,.....
- We have to find the recursive and explicit formula of the given sequence.

We have given a sequence -15,-6,-3,12,21,.....

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 9

So, The recursive formula is

Step 2 of 2:

The given sequence is an AP.

So, The explicit formula will be

### The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is perpendicular to the north path.

- We have been given an equation that represents the north path on a map.
- We have to find an equation for a path that passes through the point (6, 3) and is perpendicular to the north path.

We have given a line passes through a point (6, 3) and perpendicular to a line

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

So,

Therefore the equation of the line will be

### The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is perpendicular to the north path.

- We have been given an equation that represents the north path on a map.
- We have to find an equation for a path that passes through the point (6, 3) and is perpendicular to the north path.

We have given a line passes through a point (6, 3) 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 recursive formula and explicit formula. 62,57,52,47,42,...

- We have given a sequence 62,57,52,47,42,....
- We have to find the recursive and explicit formula of the given sequence.

We have given a sequence 62,57,52,47,42,....

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 -15

So, The recursive formula is

Step 2 of 2:

The given sequence is an AP.

So, The explicit formula will be

### Write recursive formula and explicit formula. 62,57,52,47,42,...

- We have given a sequence 62,57,52,47,42,....
- We have to find the recursive and explicit formula of the given sequence.

We have given a sequence 62,57,52,47,42,....

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 -15

So, The recursive formula is

Step 2 of 2:

The given sequence is an AP.

So, The explicit formula will be

### Write recursive formula and explicit formula. -4, 5,14,23,32,...

We have given a sequence -4,5,14,23,32,...

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 9

So, The recursive formula is

Step 2 of 2:

The given sequence is an AP.

So, The explicit formula will be

.

### Write recursive formula and explicit formula. -4, 5,14,23,32,...

We have given a sequence -4,5,14,23,32,...

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 9

So, The recursive formula is

Step 2 of 2:

The given sequence is an AP.

So, The explicit formula will be

.

### What are the vertical and horizontal asymptotes of the graph of 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 .

3x

^{2}-12= 0

3x

^{2}= 12

x

^{2}= 4

x = -2 or x = 2

The vertical asymptote of the rational function is x = −2 and x = 2

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 x = 2. and horizontal asymptote is

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

### What are the vertical and horizontal asymptotes of the graph of 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 .

3x

^{2}-12= 0

3x

^{2}= 12

x

^{2}= 4

x = -2 or x = 2

The vertical asymptote of the rational function is x = −2 and x = 2

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 x = 2. and horizontal asymptote is

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

### The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.

- We have been given an equation that represents the north path on a map.
- We have to find an equation for a path that passes through the point (6, 3) and is perpendicular to the north path.

We have given a line passes through a point (6, 3) and parallel to a line y = 2x + 7

Since two parallel lines have same slope.

So, Slope of the line will be 2

Therefore the equation of the line will be

y - 3 = 2(x - 6)

y = 2x - 9

### The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.

- We have been given an equation that represents the north path on a map.

We have given a line passes through a point (6, 3) and parallel to a line y = 2x + 7

Since two parallel lines have same slope.

So, Slope of the line will be 2

Therefore the equation of the line will be

y - 3 = 2(x - 6)

y = 2x - 9

### Write recursive formula and explicit formula. 12,19,26,33,40,...

- We have given a sequence 12,19,26,33,40,....
- We have to find the recursive and explicit formula of the given sequence.

We have given a sequence 12,19,26,33,40,....

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 7

So, The recursive formula is

Step 2 of 2:

The given sequence is an AP.

So, The explicit formula will be

.

### Write recursive formula and explicit formula. 12,19,26,33,40,...

- We have given a sequence 12,19,26,33,40,....
- We have to find the recursive and explicit formula of the given sequence.

We have given a sequence 12,19,26,33,40,....

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 7

So, The recursive formula is

Step 2 of 2:

The given sequence is an AP.

So, The explicit formula will be

.

### What are the vertical and horizontal asymptotes of the graph of each function?

- 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 - 8 = 0

x

^{2}+ 2x - 4x - 8 = 0

x(x + 2)- 4(x + 2) = 0

(x + 2)(x - 4)=0

x= -2 or x= 4

The vertical asymptote of the rational function is x =−2 and x = 4

This function has x -intercept at (-2.386,0) and y -intercept at (0,1.125) . 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. and horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) = =2

### What are the vertical and horizontal asymptotes of the graph of each function?

- 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 - 8 = 0

x

^{2}+ 2x - 4x - 8 = 0

x(x + 2)- 4(x + 2) = 0

(x + 2)(x - 4)=0

x= -2 or x= 4

The vertical asymptote of the rational function is x =−2 and x = 4

This function has x -intercept at (-2.386,0) and y -intercept at (0,1.125) . 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. and horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) = =2