Question

# Tell whether the given sequence is an arithmetic sequence. -6,5,16,27,38,....

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: ⇒11

### Explanation:

- We have given a sequence -6,5,16,27,38,....
- We have to find weather the given sequence is AP or not.

Step 1 of 1:

We have given sequence -6,5,16,27,38,....

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.

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.

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### When will the graph of a rational function have no vertical asymptotes ? Give an example of such a function.

Let's say that r is a rational function.

Identify R's domain.

If necessary, reduce r(x) to its simplest form.

Find the x- and y-intercepts of the y=r(x) graph if one exists.

If the graph contains any vertical asymptotes or holes, locate where they are.

Then, identify and, if necessary, analyze r's behavior on each side of the vertical asymptotes.

Investigate R's final behavior. If one exists, locate the horizontal or slant asymptote.

The graph of y=r(x) can be drawn using a sign diagram and additional points if necessary.

### When will the graph of a rational function have no vertical asymptotes ? Give an example of such a function.

Let's say that r is a rational function.

Identify R's domain.

If necessary, reduce r(x) to its simplest form.

Find the x- and y-intercepts of the y=r(x) graph if one exists.

If the graph contains any vertical asymptotes or holes, locate where they are.

Then, identify and, if necessary, analyze r's behavior on each side of the vertical asymptotes.

Investigate R's final behavior. If one exists, locate the horizontal or slant asymptote.

The graph of y=r(x) can be drawn using a sign diagram and additional points if necessary.