QuestionWrite an equation for the sequence $7, 9, 11, 13, 15, \ldots$ and find the 20th term.

Studdy Solution

STEP 1

Assumptions1. The sequence is arithmetic, meaning the difference between consecutive terms is constant. . The first term of the sequence is7.
3. The common difference of the sequence is (since9-7 =,11-9 =, etc.).
4. We are looking for the20th term of the sequence.

STEP 2

The general form of an arithmetic sequence can be written as $a_n = a1 + (n -1) * d$ where- $a_n$ is the nth term of the sequence, - $a1$ is the first term of the sequence, - $n$ is the term number, - $d$ is the common difference.

STEP 3

Substitute the values of $a1$ and $d$ into the general form of the arithmetic sequence.
$a_n =7 + (n -1) *2$

STEP 4

implify the equation to get the formula for any term in the sequence.
$a_n =7 +2n -2$ $a_n =2n +$

STEP 5

Now that we have the equation that describes the sequence, we can use it to find the20th term. Substitute $n =20$ into the equation.
$a_{20} =2*20 +5$

STEP 6

Calculate the20th term of the sequence.
$a_{20} =2*20 +5 =45$ The20th term of the sequence is45.

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QuestionWrite an equation for the sequence $7, 9, 11, 13, 15, \ldots$ and find the 20th term.

Studdy Solution

STEP 1

Assumptions1. The sequence is arithmetic, meaning the difference between consecutive terms is constant. . The first term of the sequence is7.
3. The common difference of the sequence is (since9-7 =,11-9 =, etc.).
4. We are looking for the20th term of the sequence.

STEP 2

The general form of an arithmetic sequence can be written as $a_n = a1 + (n -1) * d$ where- $a_n$ is the nth term of the sequence, - $a1$ is the first term of the sequence, - $n$ is the term number, - $d$ is the common difference.

STEP 3

Substitute the values of $a1$ and $d$ into the general form of the arithmetic sequence.
$a_n =7 + (n -1) *2$

STEP 4

implify the equation to get the formula for any term in the sequence.
$a_n =7 +2n -2$ $a_n =2n +$

STEP 5

Now that we have the equation that describes the sequence, we can use it to find the20th term. Substitute $n =20$ into the equation.
$a_{20} =2*20 +5$

STEP 6

Calculate the20th term of the sequence.
$a_{20} =2*20 +5 =45$ The20th term of the sequence is45.

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QuestionWrite an equation for the sequence 7,9,11,13,15,…7, 9, 11, 13, 15, \ldots7,9,11,13,15,… and find the 20th term.

Studdy Solution

STEP 1

Assumptions1. The sequence is arithmetic, meaning the difference between consecutive terms is constant. . The first term of the sequence is7.3. The common difference of the sequence is (since9-7 =,11-9 =, etc.).4. We are looking for the20th term of the sequence.

STEP 2

The general form of an arithmetic sequence can be written asan=a1+(n−1)∗da_n = a1 + (n -1) * dan​=a1+(n−1)∗dwhere- ana_nan​ is the nth term of the sequence, - a1a1a1 is the first term of the sequence, - nnn is the term number, - ddd is the common difference.

STEP 3

Substitute the values of a1a1a1 and ddd into the general form of the arithmetic sequence.an=7+(n−1)∗2a_n =7 + (n -1) *2an​=7+(n−1)∗2

STEP 4

implify the equation to get the formula for any term in the sequence.an=7+2n−2a_n =7 +2n -2an​=7+2n−2an=2n+a_n =2n +an​=2n+

STEP 5

Now that we have the equation that describes the sequence, we can use it to find the20th term. Substitute n=20n =20n=20 into the equation.a20=2∗20+5a_{20} =2*20 +5a20​=2∗20+5

STEP 6

Calculate the20th term of the sequence.a20=2∗20+5=45a_{20} =2*20 +5 =45a20​=2∗20+5=45The20th term of the sequence is45.

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

QuestionWrite an equation for the sequence $7, 9, 11, 13, 15, \ldots$ and find the 20th term.

Assumptions1. The sequence is arithmetic, meaning the difference between consecutive terms is constant. . The first term of the sequence is7.
3. The common difference of the sequence is (since9-7 =,11-9 =, etc.).
4. We are looking for the20th term of the sequence.

The general form of an arithmetic sequence can be written as $a_n = a1 + (n -1) * d$ where- $a_n$ is the nth term of the sequence, - $a1$ is the first term of the sequence, - $n$ is the term number, - $d$ is the common difference.

Substitute the values of $a1$ and $d$ into the general form of the arithmetic sequence.
$a_n =7 + (n -1) *2$

implify the equation to get the formula for any term in the sequence.
$a_n =7 +2n -2$ $a_n =2n +$

Now that we have the equation that describes the sequence, we can use it to find the20th term. Substitute $n =20$ into the equation.
$a_{20} =2*20 +5$

Calculate the20th term of the sequence.
$a_{20} =2*20 +5 =45$ The20th term of the sequence is45.