QuestionWhich function describes the sequence: -5, -7, -9, -11, -13, ...? A) $f(x)=-3x+2$ B) $f(x)=-2x+3$ C) $f(x)=-3x-2$ D) $f(x)=-2x-3$

Studdy Solution

STEP 1

Assumptions1. The given sequence is arithmetic, which means the difference between consecutive terms is constant. . The sequence given is $-5,-7,-9,-11,-13, \ldots$
3. We need to find the function that describes this sequence.

STEP 2

First, we need to find the common difference of the arithmetic sequence. We can do this by subtracting the second term from the first term.
$d = a2 - a1$

STEP 3

Now, plug in the given values for $a2$ and $a1$ to calculate the common difference.
$d = -7 - (-5)$

STEP 4

Calculate the common difference.
$d = -7 - (-) = -2$

STEP 5

An arithmetic sequence can be represented by the function $f(x) = d \cdot x + c$ , where $d$ is the common difference and $c$ is a constant.

STEP 6

We know that $d = -2$ . Now we need to find the constant $c$ . We know that the first term of the sequence is $-5$ when $x=1$ . So we can set up the equation $-5 = -2 \cdot1 + c$ and solve for $c$ .

STEP 7

olve the equation for $c$ .
$-5 = -2 \cdot1 + c$ $-5 = -2 + c$ $c = -5 +2$ $c = -3$

STEP 8

Now that we have the common difference $d$ and the constant $c$ , we can write the function that describes the arithmetic sequence.
$f(x) = -2x -3$ The function that describes the arithmetic sequence is $f(x) = -2x -3$ , which corresponds to option D.

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QuestionWhich function describes the sequence: -5, -7, -9, -11, -13, ...? A) $f(x)=-3x+2$ B) $f(x)=-2x+3$ C) $f(x)=-3x-2$ D) $f(x)=-2x-3$

Studdy Solution

STEP 1

Assumptions1. The given sequence is arithmetic, which means the difference between consecutive terms is constant. . The sequence given is $-5,-7,-9,-11,-13, \ldots$
3. We need to find the function that describes this sequence.

STEP 2

First, we need to find the common difference of the arithmetic sequence. We can do this by subtracting the second term from the first term.
$d = a2 - a1$

STEP 3

Now, plug in the given values for $a2$ and $a1$ to calculate the common difference.
$d = -7 - (-5)$

STEP 4

Calculate the common difference.
$d = -7 - (-) = -2$

STEP 5

An arithmetic sequence can be represented by the function $f(x) = d \cdot x + c$ , where $d$ is the common difference and $c$ is a constant.

STEP 6

We know that $d = -2$ . Now we need to find the constant $c$ . We know that the first term of the sequence is $-5$ when $x=1$ . So we can set up the equation $-5 = -2 \cdot1 + c$ and solve for $c$ .

STEP 7

olve the equation for $c$ .
$-5 = -2 \cdot1 + c$ $-5 = -2 + c$ $c = -5 +2$ $c = -3$

STEP 8

Now that we have the common difference $d$ and the constant $c$ , we can write the function that describes the arithmetic sequence.
$f(x) = -2x -3$ The function that describes the arithmetic sequence is $f(x) = -2x -3$ , which corresponds to option D.

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QuestionWhich function describes the sequence: -5, -7, -9, -11, -13, ...? A) f(x)=−3x+2f(x)=-3x+2f(x)=−3x+2 B) f(x)=−2x+3f(x)=-2x+3f(x)=−2x+3 C) f(x)=−3x−2f(x)=-3x-2f(x)=−3x−2 D) f(x)=−2x−3f(x)=-2x-3f(x)=−2x−3

Studdy Solution

STEP 1

Assumptions1. The given sequence is arithmetic, which means the difference between consecutive terms is constant. . The sequence given is −5,−7,−9,−11,−13,…-5,-7,-9,-11,-13, \ldots−5,−7,−9,−11,−13,…3. We need to find the function that describes this sequence.

STEP 2

First, we need to find the common difference of the arithmetic sequence. We can do this by subtracting the second term from the first term.d=a2−a1d = a2 - a1d=a2−a1

STEP 3

Now, plug in the given values for a2a2a2 and a1a1a1 to calculate the common difference.d=−7−(−5)d = -7 - (-5)d=−7−(−5)

STEP 4

Calculate the common difference.d=−7−(−)=−2d = -7 - (-) = -2d=−7−(−)=−2

STEP 5

An arithmetic sequence can be represented by the function f(x)=d⋅x+cf(x) = d \cdot x + cf(x)=d⋅x+c, where ddd is the common difference and ccc is a constant.

STEP 6

We know that d=−2d = -2d=−2. Now we need to find the constant ccc. We know that the first term of the sequence is −5-5−5 when x=1x=1x=1. So we can set up the equation −5=−2⋅1+c-5 = -2 \cdot1 + c−5=−2⋅1+c and solve for ccc.

STEP 7

olve the equation for ccc.−5=−2⋅1+c-5 = -2 \cdot1 + c−5=−2⋅1+c−5=−2+c-5 = -2 + c−5=−2+cc=−5+2c = -5 +2c=−5+2c=−3c = -3c=−3

STEP 8

Now that we have the common difference ddd and the constant ccc, we can write the function that describes the arithmetic sequence.f(x)=−2x−3f(x) = -2x -3f(x)=−2x−3The function that describes the arithmetic sequence is f(x)=−2x−3f(x) = -2x -3f(x)=−2x−3, which corresponds to option D.

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QuestionWhich function describes the sequence: -5, -7, -9, -11, -13, ...? A) $f(x)=-3x+2$ B) $f(x)=-2x+3$ C) $f(x)=-3x-2$ D) $f(x)=-2x-3$

Assumptions1. The given sequence is arithmetic, which means the difference between consecutive terms is constant. . The sequence given is $-5,-7,-9,-11,-13, \ldots$
3. We need to find the function that describes this sequence.

First, we need to find the common difference of the arithmetic sequence. We can do this by subtracting the second term from the first term.
$d = a2 - a1$

Now, plug in the given values for $a2$ and $a1$ to calculate the common difference.
$d = -7 - (-5)$

Calculate the common difference.
$d = -7 - (-) = -2$

An arithmetic sequence can be represented by the function $f(x) = d \cdot x + c$ , where $d$ is the common difference and $c$ is a constant.

We know that $d = -2$ . Now we need to find the constant $c$ . We know that the first term of the sequence is $-5$ when $x=1$ . So we can set up the equation $-5 = -2 \cdot1 + c$ and solve for $c$ .

olve the equation for $c$ .
$-5 = -2 \cdot1 + c$ $-5 = -2 + c$ $c = -5 +2$ $c = -3$

Now that we have the common difference $d$ and the constant $c$ , we can write the function that describes the arithmetic sequence.
$f(x) = -2x -3$ The function that describes the arithmetic sequence is $f(x) = -2x -3$ , which corresponds to option D.