Question
Write recursive formula. -5,-8.5,-12,-15.5,-19,....
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=a_(n-1)-3.5.
Explanation:
- We have given a sequence -5,-8.5,-12,-15.5,-19,....
- We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given a sequence -5,-8.5,-12,-15.5,-19,....
The given sequence is an AP
And we know the recursive formula of any AP is
.
Where d is common difference.
Here the common difference is -3.5.
So, The recursive formula is
![a subscript n equals a subscript n minus 1 end subscript minus 3.5](data:image/png;base64,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)
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Tell whether the given sequence is an arithmetic sequence. 48,45,42,39,....
Find the vertical and horizontal asymptotes of rational function, then graph the function.
![straight F left parenthesis straight x right parenthesis equals fraction numerator x plus 2 over denominator x minus 3 end fraction](data:image/png;base64,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)
Find the vertical and horizontal asymptotes of rational function, then graph the function.
![straight F left parenthesis straight x right parenthesis equals fraction numerator x plus 2 over denominator x minus 3 end fraction](data:image/png;base64,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)
Which sequence is an arithmetic sequence?
Which sequence is an arithmetic sequence?
Write an equation of a line that passes through the given line and is perpendicular to the given line.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbgAAAAyCAYAAAAuls65AAABPUlEQVR4nO3bMYqEMACF4VVXPIqVjfe/hacRwUy/hB2LjDKP7ytDitf9BLQrpZQfAAjTPz0AAD5B4ACIJHAARBI4ACIJHACRBA6ASAIHQCSBAyCSwAEQSeAAiCRwAEQSOAAiCRwAkQQOgEgCB0AkgQMgksABEEngAIgkcABEEjgAIv3WDpdluXsHALy1bdvlu10ppfw9HMex6SAAaOE4jst3qy+4eZ6bjQGAJ1QDNwzD3TsAoKlq4PretycAfDeBAyBSNXBd1929AwCa8lQDIFL1BXee5907AKCp6n9w0zQ9sQUA/rXv++W71Rfcuq7NxgDAE6ovOAD4dj4yASCSwAEQSeAAiCRwAEQSOAAiCRwAkQQOgEgCB0AkgQMgksABEEngAIgkcABEEjgAIgkcAJEEDoBIAgdAJIEDINILyn0dfvj+7mMAAAAASUVORK5CYII=)
![left parenthesis negative 6 comma negative 3 right parenthesis semicolon y equals negative 2 over 5 x](data:image/png;base64,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)
Write an equation of a line that passes through the given line and is perpendicular to the given line.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbgAAAAyCAYAAAAuls65AAABPUlEQVR4nO3bMYqEMACF4VVXPIqVjfe/hacRwUy/hB2LjDKP7ytDitf9BLQrpZQfAAjTPz0AAD5B4ACIJHAARBI4ACIJHACRBA6ASAIHQCSBAyCSwAEQSeAAiCRwAEQSOAAiCRwAkQQOgEgCB0AkgQMgksABEEngAIgkcABEEjgAIv3WDpdluXsHALy1bdvlu10ppfw9HMex6SAAaOE4jst3qy+4eZ6bjQGAJ1QDNwzD3TsAoKlq4PretycAfDeBAyBSNXBd1929AwCa8lQDIFL1BXee5907AKCp6n9w0zQ9sQUA/rXv++W71Rfcuq7NxgDAE6ovOAD4dj4yASCSwAEQSeAAiCRwAEQSOAAiCRwAkQQOgEgCB0AkgQMgksABEEngAIgkcABEEjgAIgkcAJEEDoBIAgdAJIEDINILyn0dfvj+7mMAAAAASUVORK5CYII=)
![left parenthesis negative 6 comma negative 3 right parenthesis semicolon y equals negative 2 over 5 x](data:image/png;base64,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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.