QuestionFind the formula for the sequence $a_{n}=\{3,6,9,12, \ldots\}$ . Options: $a_{n}=3 n$ , $a_{3}=3_{a}$ , $a_{n}=9 n$ , $a_{n}=6_{n}$ .

Studdy Solution

STEP 1

Assumptions1. The sequence is arithmetic, meaning it increases by a constant difference. . The first term of the sequence is3.
3. The common difference of the sequence is the difference between any two consecutive terms.

STEP 2

We can observe that the sequence increases by each time. This is the common difference of the sequence.
$Common\, difference = a_{n+1} - a_{n} =$

STEP 3

In an arithmetic sequence, the nth term can be found using the formula $a_{n} = a_{1} + (n -1) \cdot d$ where $a_{1}$ is the first term, $d$ is the common difference, and $n$ is the term number.

STEP 4

Substitute the values of $a_{1}$ and $d$ into the formula.
$a_{n} =3 + (n -1) \cdot3$

STEP 5

implify the formula.
$a_{n} =3n$ The formula for the sequence $a_{n}=\{3,,9,12, \ldots\}$ is $a_{n}=3n$ .

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QuestionFind the formula for the sequence $a_{n}=\{3,6,9,12, \ldots\}$ . Options: $a_{n}=3 n$ , $a_{3}=3_{a}$ , $a_{n}=9 n$ , $a_{n}=6_{n}$ .

Studdy Solution

STEP 1

Assumptions1. The sequence is arithmetic, meaning it increases by a constant difference. . The first term of the sequence is3.
3. The common difference of the sequence is the difference between any two consecutive terms.

STEP 2

We can observe that the sequence increases by each time. This is the common difference of the sequence.
$Common\, difference = a_{n+1} - a_{n} =$

STEP 3

In an arithmetic sequence, the nth term can be found using the formula $a_{n} = a_{1} + (n -1) \cdot d$ where $a_{1}$ is the first term, $d$ is the common difference, and $n$ is the term number.

STEP 4

Substitute the values of $a_{1}$ and $d$ into the formula.
$a_{n} =3 + (n -1) \cdot3$

STEP 5

implify the formula.
$a_{n} =3n$ The formula for the sequence $a_{n}=\{3,,9,12, \ldots\}$ is $a_{n}=3n$ .

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QuestionFind the formula for the sequence an={3,6,9,12,…}a_{n}=\{3,6,9,12, \ldots\}an​={3,6,9,12,…}. Options: an=3na_{n}=3 nan​=3n, a3=3aa_{3}=3_{a}a3​=3a​, an=9na_{n}=9 nan​=9n, an=6na_{n}=6_{n}an​=6n​.

Studdy Solution

STEP 1

Assumptions1. The sequence is arithmetic, meaning it increases by a constant difference. . The first term of the sequence is3.3. The common difference of the sequence is the difference between any two consecutive terms.

STEP 2

We can observe that the sequence increases by each time. This is the common difference of the sequence.Common difference=an+1−an=Common\, difference = a_{n+1} - a_{n} =Commondifference=an+1​−an​=

STEP 3

In an arithmetic sequence, the nth term can be found using the formulaan=a1+(n−1)⋅da_{n} = a_{1} + (n -1) \cdot dan​=a1​+(n−1)⋅dwhere a1a_{1}a1​ is the first term, ddd is the common difference, and nnn is the term number.

STEP 4

Substitute the values of a1a_{1}a1​ and ddd into the formula.an=3+(n−1)⋅3a_{n} =3 + (n -1) \cdot3an​=3+(n−1)⋅3

STEP 5

implify the formula.an=3na_{n} =3nan​=3nThe formula for the sequence an={3,,9,12,…}a_{n}=\{3,,9,12, \ldots\}an​={3,,9,12,…} is an=3na_{n}=3nan​=3n.

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QuestionFind the formula for the sequence $a_{n}=\{3,6,9,12, \ldots\}$ . Options: $a_{n}=3 n$ , $a_{3}=3_{a}$ , $a_{n}=9 n$ , $a_{n}=6_{n}$ .

Assumptions1. The sequence is arithmetic, meaning it increases by a constant difference. . The first term of the sequence is3.
3. The common difference of the sequence is the difference between any two consecutive terms.

We can observe that the sequence increases by each time. This is the common difference of the sequence.
$Common\, difference = a_{n+1} - a_{n} =$

In an arithmetic sequence, the nth term can be found using the formula $a_{n} = a_{1} + (n -1) \cdot d$ where $a_{1}$ is the first term, $d$ is the common difference, and $n$ is the term number.

Substitute the values of $a_{1}$ and $d$ into the formula.
$a_{n} =3 + (n -1) \cdot3$

implify the formula.
$a_{n} =3n$ The formula for the sequence $a_{n}=\{3,,9,12, \ldots\}$ is $a_{n}=3n$ .