QuestionFind the explicit formula for the sequence: 15, 19, 23, 27, ...

Studdy Solution

STEP 1

Assumptions1. The sequence given is an arithmetic sequence, as the difference between successive terms is constant. . The first term of the sequence is15.
3. The common difference of the sequence is4 (19 -15 =4).

STEP 2

The explicit formula for an arithmetic sequence is given by $a_n = a1 + (n -1) \cdot d$ where- $a_n$ is the nth term of the sequence, - $a1$ is the first term of the sequence, - $d$ is the common difference, and- $n$ is the term number.

STEP 3

Substitute the values of $a1$ and $d$ into the formula.
$a_n =15 + (n -1) \cdot$

STEP 4

implify the formula.
$a_n =15 +4n -4$

STEP 5

Combine like terms.
$a_n =11 +4n$ So, the explicit formula for the given arithmetic sequence is $a_n =11 +4n$ .

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QuestionFind the explicit formula for the sequence: 15, 19, 23, 27, ...

Studdy Solution

STEP 1

Assumptions1. The sequence given is an arithmetic sequence, as the difference between successive terms is constant. . The first term of the sequence is15.
3. The common difference of the sequence is4 (19 -15 =4).

STEP 2

The explicit formula for an arithmetic sequence is given by $a_n = a1 + (n -1) \cdot d$ where- $a_n$ is the nth term of the sequence, - $a1$ is the first term of the sequence, - $d$ is the common difference, and- $n$ is the term number.

STEP 3

Substitute the values of $a1$ and $d$ into the formula.
$a_n =15 + (n -1) \cdot$

STEP 4

implify the formula.
$a_n =15 +4n -4$

STEP 5

Combine like terms.
$a_n =11 +4n$ So, the explicit formula for the given arithmetic sequence is $a_n =11 +4n$ .

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QuestionFind the explicit formula for the sequence: 15, 19, 23, 27, ...

Studdy Solution

STEP 1

Assumptions1. The sequence given is an arithmetic sequence, as the difference between successive terms is constant. . The first term of the sequence is15.3. The common difference of the sequence is4 (19 -15 =4).

STEP 2

The explicit formula for an arithmetic sequence is given byan=a1+(n−1)⋅da_n = a1 + (n -1) \cdot dan​=a1+(n−1)⋅dwhere- ana_nan​ is the nth term of the sequence, - a1a1a1 is the first term of the sequence, - ddd is the common difference, and- nnn is the term number.

STEP 3

Substitute the values of a1a1a1 and ddd into the formula.an=15+(n−1)⋅a_n =15 + (n -1) \cdotan​=15+(n−1)⋅

STEP 4

implify the formula.an=15+4n−4a_n =15 +4n -4an​=15+4n−4

STEP 5

Combine like terms.an=11+4na_n =11 +4nan​=11+4nSo, the explicit formula for the given arithmetic sequence is an=11+4na_n =11 +4nan​=11+4n.

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Assumptions1. The sequence given is an arithmetic sequence, as the difference between successive terms is constant. . The first term of the sequence is15.
3. The common difference of the sequence is4 (19 -15 =4).

The explicit formula for an arithmetic sequence is given by $a_n = a1 + (n -1) \cdot d$ where- $a_n$ is the nth term of the sequence, - $a1$ is the first term of the sequence, - $d$ is the common difference, and- $n$ is the term number.

Substitute the values of $a1$ and $d$ into the formula.
$a_n =15 + (n -1) \cdot$

implify the formula.
$a_n =15 +4n -4$

Combine like terms.
$a_n =11 +4n$ So, the explicit formula for the given arithmetic sequence is $a_n =11 +4n$ .