Question
Which arithmetic sequence is described by the linear function f(n)=12n−13
?(1 point)
Responses
−13,−252,−12 . . .
negative 13 comma negative Start Fraction 25 over 2 End Fraction comma negative 12 dot dot dot
−25/2,−23/2,−21/2 . . .
negative Start Fraction 25 over 2 End Fraction comma negative Start Fraction 23 over 2 End Fraction comma negative Start Fraction 21 over 2 End Fraction dot dot dot
−252,−12,−232 . . .
negative Start Fraction 25 over 2 End Fraction comma negative 12 comma negative Start Fraction 23 over 2 End Fraction dot dot dot
272,14,292 . . .
?(1 point)
Responses
−13,−252,−12 . . .
negative 13 comma negative Start Fraction 25 over 2 End Fraction comma negative 12 dot dot dot
−25/2,−23/2,−21/2 . . .
negative Start Fraction 25 over 2 End Fraction comma negative Start Fraction 23 over 2 End Fraction comma negative Start Fraction 21 over 2 End Fraction dot dot dot
−252,−12,−232 . . .
negative Start Fraction 25 over 2 End Fraction comma negative 12 comma negative Start Fraction 23 over 2 End Fraction dot dot dot
272,14,292 . . .
Answers
Answered by
GPT-4o mini
To determine which arithmetic sequence is described by the linear function \( f(n) = 12n - 13 \), we need to calculate the first few terms of the sequence by plugging in values for \( n \).
1. For \( n = 1 \):
\[
f(1) = 12(1) - 13 = 12 - 13 = -1
\]
2. For \( n = 2 \):
\[
f(2) = 12(2) - 13 = 24 - 13 = 11
\]
3. For \( n = 3 \):
\[
f(3) = 12(3) - 13 = 36 - 13 = 23
\]
So the first three terms of the sequence are:
- \( -1 \) (for \( n = 1 \))
- \( 11 \) (for \( n = 2 \))
- \( 23 \) (for \( n = 3 \))
Now, let's double-check the given sequences:
1. \( -13, -\frac{25}{2}, -12, \ldots \)
2. \( -\frac{25}{2}, -\frac{23}{2}, -\frac{21}{2}, \ldots \)
3. \( -\frac{25}{2}, -12, -\frac{23}{2}, \ldots \)
4. \( 272, 14, 292, \ldots \)
None of these sequences match the values \( -1, 11, 23 \).
Let's check the function more closely. Since it is a linear function, it has a specific common difference (in this case, the coefficient of \( n \), which is \( 12 \)).
The nth-term formula \( f(n) = 12n - 13 \) produces terms that increase by \( 12 \) each time:
- From \( -1 \) to \( 11 \), the difference is \( 11 - (-1) = 12 \).
- From \( 11 \) to \( 23 \), the difference is again \( 23 - 11 = 12 \).
If the arithmetic sequence starts at \( f(1) = -1 \):
- The first term is \( -1 \)
- The second term would be \( -1 + 12 = 11 \)
- The third term would be \( 11 + 12 = 23 \)
Thus the sequence can be alternatively expressed as \( -1, 11, 23, \ldots \):
This doesn't match exactly with any given answer choice.
However, to slightly adjust the look of one of the sequences provided, remember the formula starting point of the sequence begins at \( n=1 \) results in a -1 constant.
Since none of the sequences provided fit or directly translate from this function and its outputs, there's no accurate answer from those listed based on the output of \( f(n) \).
1. For \( n = 1 \):
\[
f(1) = 12(1) - 13 = 12 - 13 = -1
\]
2. For \( n = 2 \):
\[
f(2) = 12(2) - 13 = 24 - 13 = 11
\]
3. For \( n = 3 \):
\[
f(3) = 12(3) - 13 = 36 - 13 = 23
\]
So the first three terms of the sequence are:
- \( -1 \) (for \( n = 1 \))
- \( 11 \) (for \( n = 2 \))
- \( 23 \) (for \( n = 3 \))
Now, let's double-check the given sequences:
1. \( -13, -\frac{25}{2}, -12, \ldots \)
2. \( -\frac{25}{2}, -\frac{23}{2}, -\frac{21}{2}, \ldots \)
3. \( -\frac{25}{2}, -12, -\frac{23}{2}, \ldots \)
4. \( 272, 14, 292, \ldots \)
None of these sequences match the values \( -1, 11, 23 \).
Let's check the function more closely. Since it is a linear function, it has a specific common difference (in this case, the coefficient of \( n \), which is \( 12 \)).
The nth-term formula \( f(n) = 12n - 13 \) produces terms that increase by \( 12 \) each time:
- From \( -1 \) to \( 11 \), the difference is \( 11 - (-1) = 12 \).
- From \( 11 \) to \( 23 \), the difference is again \( 23 - 11 = 12 \).
If the arithmetic sequence starts at \( f(1) = -1 \):
- The first term is \( -1 \)
- The second term would be \( -1 + 12 = 11 \)
- The third term would be \( 11 + 12 = 23 \)
Thus the sequence can be alternatively expressed as \( -1, 11, 23, \ldots \):
This doesn't match exactly with any given answer choice.
However, to slightly adjust the look of one of the sequences provided, remember the formula starting point of the sequence begins at \( n=1 \) results in a -1 constant.
Since none of the sequences provided fit or directly translate from this function and its outputs, there's no accurate answer from those listed based on the output of \( f(n) \).