Maths-
General
Easy

Question

Tell whether the given sequence is an arithmetic sequence. 93,86,79,72,66,...

Hint:

General
Maths-

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.
Step 1 of 1:
We have given two equations

Slope of both lines are 2, respectively
Since slope are not equal then both are not parallel.
Product of both slope is
So, both are not perpendicular also.
So,
Both are nor parallel neither perpendicular.

Are graphs of the equations parallel, perpendicular or neither?

Maths-General
• We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
Step 1 of 1:
We have given two equations

Slope of both lines are 2, respectively
Since slope are not equal then both are not parallel.
Product of both slope is
So, both are not perpendicular also.
So,
Both are nor parallel neither perpendicular.

General
Maths-

Tell whether the given sequence is an arithmetic sequence. 37,3,31,29,26,23,...

• We have given a sequence 37,34,31,29,26,23,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 37,34,31,29,26,23,...
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 constant
The given sequence is an arithmetic sequence.

Tell whether the given sequence is an arithmetic sequence. 37,3,31,29,26,23,...

Maths-General
• We have given a sequence 37,34,31,29,26,23,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 37,34,31,29,26,23,...
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 constant
The given sequence is an arithmetic sequence.

General
Maths-

What are the horizontal asymptotes for 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 .
x2 + 7x + 12 = 0
x2 + 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 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.

What are the horizontal asymptotes for the graph

Maths-General
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 .
x2 + 7x + 12 = 0
x2 + 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 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.
General
Maths-

Tell whether the given sequence is an arithmetic sequence. 3,6,9,15,18,...

• We have given a sequence 3,6,9,15,18,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 3,6,9,15,18,...
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.

Tell whether the given sequence is an arithmetic sequence. 3,6,9,15,18,...

Maths-General
• We have given a sequence 3,6,9,15,18,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 3,6,9,15,18,...
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.

General
Maths-

Tell whether the given sequence is an arithmetic sequence. 3,6,9,12,15,18,...

• We have given a sequence 3,6,9,12,15,18,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 3,6,9,12,15,18,...
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 constant
The given sequence is an arithmetic sequence.

Tell whether the given sequence is an arithmetic sequence. 3,6,9,12,15,18,...

Maths-General
• We have given a sequence 3,6,9,12,15,18,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 3,6,9,12,15,18,...
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 constant
The given sequence is an arithmetic sequence.

General
Maths-

Tell whether the given sequence is an arithmetic sequence. 1,-2,3,-4,5,...

• We have given a sequence
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence
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.

Tell whether the given sequence is an arithmetic sequence. 1,-2,3,-4,5,...

Maths-General
• We have given a sequence
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence
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.

General
Maths-

Tell whether the given sequence is an arithmetic sequence. 77,64,51,38,25,...

• We have given a sequence 77,64,51,38,25,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 77,64,51,38,25,..
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 constant
The given sequence is an arithmetic sequence.

Tell whether the given sequence is an arithmetic sequence. 77,64,51,38,25,...

Maths-General
• We have given a sequence 77,64,51,38,25,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 77,64,51,38,25,..
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 constant
The given sequence is an arithmetic sequence.

General
Maths-

Tell whether the given sequence is an arithmetic sequence. 1,15,29,43,57,....

• We have given a sequence 1,15,29,43,57,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 1,15,29,43,57,...
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 constant
The given sequence is an arithmetic sequence.

Tell whether the given sequence is an arithmetic sequence. 1,15,29,43,57,....

Maths-General
• We have given a sequence 1,15,29,43,57,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 1,15,29,43,57,...
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 constant
The given sequence is an arithmetic sequence.

General
Maths-

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

• 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

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

Maths-General
• 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

General
Maths-

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

Explanation:
• We have given a sequence 81,85,89,93,97,...
• We have to find the recursive formula.
Step 1 of 1:
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,...
• We have to find the recursive formula.
Step 1 of 1:
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

General
Maths-

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

Explanation:
• We have given a sequence 4,7,10,14,..
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
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,....

Maths-General
Explanation:
• We have given a sequence 4,7,10,14,..
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
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.
General
Maths-

How do you find vertical and horizontal asymptotes of a rational function? What are the vertical asymptotes for the graph of

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 .
x2 +7x + 12 = 0
x2 + 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

Maths-General
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 .
x2 +7x + 12 = 0
x2 + 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.
General
Maths-

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.
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.

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

Maths-General
• 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.

General
Maths-

Write an explicit formula for the arithmetic sequence.an = 12 - 5n

• We have given an explicit formula an = 12 - 5n
• We have to find the recursive formula
Step 1 of 1:
We have given a explicit formula an = 12 - 5n

Now,

So, The recursive formula is .

Write an explicit formula for the arithmetic sequence.an = 12 - 5n

Maths-General
• We have given an explicit formula an = 12 - 5n
• We have to find the recursive formula
Step 1 of 1:
We have given a explicit formula an = 12 - 5n

Now,

So, The recursive formula is .

General
Maths-

Write an explicit formula for the arithmetic sequence.an = 8 + 3n

• We have given an explicit formula an = 8 + 3n
• We have to find the recursive formula
Step 1 of 1:
We have given a explicit formula an = 8 + 3n

Now,

So, The recursive formula is .

Write an explicit formula for the arithmetic sequence.an = 8 + 3n

Maths-General
• We have given an explicit formula an = 8 + 3n
• We have to find the recursive formula
Step 1 of 1:
We have given a explicit formula an = 8 + 3n

Now,

So, The recursive formula is .