QuestionFind the explicit formula for the arithmetic sequence starting with $a_{1}=54$ and the first six terms: $54, 73, 92, 111, 130, 149$ .

Studdy Solution

STEP 1

Assumptions1. The sequence is an arithmetic sequence. The first term of the sequence, $a_{1}$ , is543. The sequence is increasing

STEP 2

In an arithmetic sequence, the difference between any two successive terms is constant. This constant difference is called the common difference, denoted by $d$ . We can find $d$ by subtracting the first term from the second term.
$d = a_{2} - a_{1}$

STEP 3

Now, plug in the given values for $a_{1}$ and $a_{2}$ to calculate the common difference.
$d =73 -54$

STEP 4

Calculate the common difference.
$d =73 -54 =19$

STEP 5

The explicit formula for an arithmetic sequence is given by $a_{n} = a_{1} + (n -1) \cdot d$ where- $a_{n}$ is the nth term of the sequence- $a_{1}$ is the first term of the sequence- $d$ is the common difference- $n$ is the term number

STEP 6

Now, plug in the given values for $a_{1}$ and $d$ into the formula.
$a_{n} =54 + (n -1) \cdot19$ So, the explicit formula for this sequence is $a_{n} =54 + (n -1) \cdot19$ .

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QuestionFind the explicit formula for the arithmetic sequence starting with $a_{1}=54$ and the first six terms: $54, 73, 92, 111, 130, 149$ .

Studdy Solution

STEP 1

Assumptions1. The sequence is an arithmetic sequence. The first term of the sequence, $a_{1}$ , is543. The sequence is increasing

STEP 2

In an arithmetic sequence, the difference between any two successive terms is constant. This constant difference is called the common difference, denoted by $d$ . We can find $d$ by subtracting the first term from the second term.
$d = a_{2} - a_{1}$

STEP 3

Now, plug in the given values for $a_{1}$ and $a_{2}$ to calculate the common difference.
$d =73 -54$

STEP 4

Calculate the common difference.
$d =73 -54 =19$

STEP 5

The explicit formula for an arithmetic sequence is given by $a_{n} = a_{1} + (n -1) \cdot d$ where- $a_{n}$ is the nth term of the sequence- $a_{1}$ is the first term of the sequence- $d$ is the common difference- $n$ is the term number

STEP 6

Now, plug in the given values for $a_{1}$ and $d$ into the formula.
$a_{n} =54 + (n -1) \cdot19$ So, the explicit formula for this sequence is $a_{n} =54 + (n -1) \cdot19$ .

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QuestionFind the explicit formula for the arithmetic sequence starting with a1=54a_{1}=54a1​=54 and the first six terms: 54,73,92,111,130,14954, 73, 92, 111, 130, 14954,73,92,111,130,149.

Studdy Solution

STEP 1

Assumptions1. The sequence is an arithmetic sequence. The first term of the sequence, a1a_{1}a1​, is543. The sequence is increasing

STEP 2

In an arithmetic sequence, the difference between any two successive terms is constant. This constant difference is called the common difference, denoted by ddd. We can find ddd by subtracting the first term from the second term.d=a2−a1d = a_{2} - a_{1}d=a2​−a1​

STEP 3

Now, plug in the given values for a1a_{1}a1​ and a2a_{2}a2​ to calculate the common difference.d=73−54d =73 -54d=73−54

STEP 4

Calculate the common difference.d=73−54=19d =73 -54 =19d=73−54=19

STEP 5

The explicit formula for an arithmetic sequence is given byan=a1+(n−1)⋅da_{n} = a_{1} + (n -1) \cdot dan​=a1​+(n−1)⋅dwhere- ana_{n}an​ is the nth term of the sequence- a1a_{1}a1​ is the first term of the sequence- ddd is the common difference- nnn is the term number

STEP 6

Now, plug in the given values for a1a_{1}a1​ and ddd into the formula.an=54+(n−1)⋅19a_{n} =54 + (n -1) \cdot19an​=54+(n−1)⋅19So, the explicit formula for this sequence is an=54+(n−1)⋅19a_{n} =54 + (n -1) \cdot19an​=54+(n−1)⋅19.

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QuestionFind the explicit formula for the arithmetic sequence starting with $a_{1}=54$ and the first six terms: $54, 73, 92, 111, 130, 149$ .

Assumptions1. The sequence is an arithmetic sequence. The first term of the sequence, $a_{1}$ , is543. The sequence is increasing

In an arithmetic sequence, the difference between any two successive terms is constant. This constant difference is called the common difference, denoted by $d$ . We can find $d$ by subtracting the first term from the second term.
$d = a_{2} - a_{1}$

Now, plug in the given values for $a_{1}$ and $a_{2}$ to calculate the common difference.
$d =73 -54$

Calculate the common difference.
$d =73 -54 =19$

The explicit formula for an arithmetic sequence is given by $a_{n} = a_{1} + (n -1) \cdot d$ where- $a_{n}$ is the nth term of the sequence- $a_{1}$ is the first term of the sequence- $d$ is the common difference- $n$ is the term number

Now, plug in the given values for $a_{1}$ and $d$ into the formula.
$a_{n} =54 + (n -1) \cdot19$ So, the explicit formula for this sequence is $a_{n} =54 + (n -1) \cdot19$ .