QuestionWhich function represents the sequence $3, 7, 11, 15, 19, 23, \ldots$ ? A) $f(x)=4x-4$ , B) $f(x)=4x-3$ , C) $f(x)=4x-2$ , D) $f(x)=4x-1$ .

Studdy Solution

STEP 1

Assumptions1. The given sequence is an arithmetic sequence, which means the difference between consecutive terms is constant. . The sequence given is $3,7,11,15,19,23, \ldots$
3. We have 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 first term from the second term.
$Common\, difference = Second\, term - First\, term$

STEP 3

Now, plug in the given values for the first term and second term to calculate the common difference.
$Common\, difference =7 -3$

STEP 4

Calculate the common difference.
$Common\, difference =7 -3 =4$

STEP 5

Now that we have the common difference, we can write the general form of an arithmetic sequence. The nth term of an arithmetic sequence can be given by $a_n = a1 + (n-1)d$ where $a_n$ is the nth term, $a1$ is the first term, $n$ is the term number, and $d$ is the common difference.

STEP 6

Plug in the values for the first term and the common difference into the general form.
$a_n =3 + (n-1)4$

STEP 7

implify the equation.
$a_n =3 +4n -4$

STEP 8

Further simplify the equation.
$a_n =4n -1$ This is the function that describes the given arithmetic sequence, which corresponds to option D.

Was this helpful?

QuestionWhich function represents the sequence $3, 7, 11, 15, 19, 23, \ldots$ ? A) $f(x)=4x-4$ , B) $f(x)=4x-3$ , C) $f(x)=4x-2$ , D) $f(x)=4x-1$ .

Studdy Solution

STEP 1

Assumptions1. The given sequence is an arithmetic sequence, which means the difference between consecutive terms is constant. . The sequence given is $3,7,11,15,19,23, \ldots$
3. We have 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 first term from the second term.
$Common\, difference = Second\, term - First\, term$

STEP 3

Now, plug in the given values for the first term and second term to calculate the common difference.
$Common\, difference =7 -3$

STEP 4

Calculate the common difference.
$Common\, difference =7 -3 =4$

STEP 5

Now that we have the common difference, we can write the general form of an arithmetic sequence. The nth term of an arithmetic sequence can be given by $a_n = a1 + (n-1)d$ where $a_n$ is the nth term, $a1$ is the first term, $n$ is the term number, and $d$ is the common difference.

STEP 6

Plug in the values for the first term and the common difference into the general form.
$a_n =3 + (n-1)4$

STEP 7

implify the equation.
$a_n =3 +4n -4$

STEP 8

Further simplify the equation.
$a_n =4n -1$ This is the function that describes the given arithmetic sequence, which corresponds to option D.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWhich function represents the sequence 3,7,11,15,19,23,…3, 7, 11, 15, 19, 23, \ldots3,7,11,15,19,23,…? A) f(x)=4x−4f(x)=4x-4f(x)=4x−4, B) f(x)=4x−3f(x)=4x-3f(x)=4x−3, C) f(x)=4x−2f(x)=4x-2f(x)=4x−2, D) f(x)=4x−1f(x)=4x-1f(x)=4x−1.

Studdy Solution

STEP 1

Assumptions1. The given sequence is an arithmetic sequence, which means the difference between consecutive terms is constant. . The sequence given is 3,7,11,15,19,23,…3,7,11,15,19,23, \ldots3,7,11,15,19,23,…3. We have 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 first term from the second term.Common difference=Second term−First termCommon\, difference = Second\, term - First\, termCommondifference=Secondterm−Firstterm

STEP 3

Now, plug in the given values for the first term and second term to calculate the common difference.Common difference=7−3Common\, difference =7 -3Commondifference=7−3

STEP 4

Calculate the common difference.Common difference=7−3=4Common\, difference =7 -3 =4Commondifference=7−3=4

STEP 5

STEP 6

Plug in the values for the first term and the common difference into the general form.an=3+(n−1)4a_n =3 + (n-1)4an​=3+(n−1)4

STEP 7

implify the equation.an=3+4n−4a_n =3 +4n -4an​=3+4n−4

STEP 8

Further simplify the equation.an=4n−1a_n =4n -1an​=4n−1This is the function that describes the given arithmetic sequence, which corresponds to option D.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWhich function represents the sequence $3, 7, 11, 15, 19, 23, \ldots$ ? A) $f(x)=4x-4$ , B) $f(x)=4x-3$ , C) $f(x)=4x-2$ , D) $f(x)=4x-1$ .

Assumptions1. The given sequence is an arithmetic sequence, which means the difference between consecutive terms is constant. . The sequence given is $3,7,11,15,19,23, \ldots$
3. We have 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 first term from the second term.
$Common\, difference = Second\, term - First\, term$

Now, plug in the given values for the first term and second term to calculate the common difference.
$Common\, difference =7 -3$

Calculate the common difference.
$Common\, difference =7 -3 =4$

Plug in the values for the first term and the common difference into the general form.
$a_n =3 + (n-1)4$

implify the equation.
$a_n =3 +4n -4$

Further simplify the equation.
$a_n =4n -1$ This is the function that describes the given arithmetic sequence, which corresponds to option D.