QuestionIdentify the function for the sequence: $-4, 0, 4, 8, 12, 16, \ldots$ from options A-D.

Studdy Solution

STEP 1

Assumptions1. The given sequence is $-4,0,4,8,12,16, \ldots$ . We are looking for a function that describes this arithmetic sequence3. The options given are $f(x)=4 x+8$ , $f(x)=4 x-8$ , $f(x)=-4 x+8$ , and $f(x)=-4 x-8$
4. In an arithmetic sequence, the difference between consecutive terms is constant

STEP 2

First, let's find the common difference of the given arithmetic sequence. The common difference in an arithmetic sequence is the difference between any term and the previous term.
$d = a_{n} - a_{n-1}$

STEP 3

Now, plug in the given values for the second term and the first term to calculate the common difference.
$d = a_{2} - a_{1} =0 - (-)$

STEP 4

Calculate the common difference.
$d =0 - (-4) =4$

STEP 5

The common difference is4. This means the coefficient of $x$ in the function should be4. So, we can eliminate options C and D.

STEP 6

Now, let's find the zeroth term (let's call it $a0$ ) of the sequence. In an arithmetic sequence, the zeroth term can be found by subtracting the common difference from the first term.
$a0 = a_{1} - d$

STEP 7

Now, plug in the given values for the first term and the common difference to calculate the zeroth term.
$a0 = a_{1} - d = -4 -4$

STEP 8

Calculate the zeroth term.
$a0 = -4 -4 = -8$

STEP 9

The zeroth term is -8. This means the constant term in the function should be -8. So, we can eliminate option A.

STEP 10

So, the function that describes the given arithmetic sequence is $f(x)=4 x-8$ .

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