QuestionFind the 47th term of the sequence given by $a_{n}=-11+(n-1)(-3)$ . Options: A. -149 B. -152 C. 127 D. -138

Studdy Solution

STEP 1

Assumptions1. The explicit formula for the arithmetic sequence is $a_{n}=-11+(n-1)(-3)$ . We are looking for the47th term of the sequence, i.e., $n=47$

STEP 2

The explicit formula for an arithmetic sequence is given as $a_{n}=a_{1}+(n-1)d$ , where $a_{1}$ is the first term, $d$ is the common difference, and $n$ is the term number. In our case, the given formula is $a_{n}=-11+(n-1)(-)$ .

STEP 3

We can see that the first term $a_{1}$ is -11 and the common difference $d$ is -3. We are asked to find the47th term, so we substitute $n=47$ into the formula.
$a_{47}=-11+(47-1)(-3)$

STEP 4

First, simplify the expression inside the parentheses.
$a_{47}=-11+(46)(-3)$

STEP 5

Next, perform the multiplication.
$a_{47}=-11+(-138)$

STEP 6

Finally, perform the addition to find the47th term.
$a_{47}=-11-138=-149$ So, the47th term of the arithmetic sequence is -149.
The correct answer is A. -149.

Was this helpful?

QuestionFind the 47th term of the sequence given by $a_{n}=-11+(n-1)(-3)$ . Options: A. -149 B. -152 C. 127 D. -138

Studdy Solution

STEP 1

Assumptions1. The explicit formula for the arithmetic sequence is $a_{n}=-11+(n-1)(-3)$ . We are looking for the47th term of the sequence, i.e., $n=47$

STEP 2

The explicit formula for an arithmetic sequence is given as $a_{n}=a_{1}+(n-1)d$ , where $a_{1}$ is the first term, $d$ is the common difference, and $n$ is the term number. In our case, the given formula is $a_{n}=-11+(n-1)(-)$ .

STEP 3

We can see that the first term $a_{1}$ is -11 and the common difference $d$ is -3. We are asked to find the47th term, so we substitute $n=47$ into the formula.
$a_{47}=-11+(47-1)(-3)$

STEP 4

First, simplify the expression inside the parentheses.
$a_{47}=-11+(46)(-3)$

STEP 5

Next, perform the multiplication.
$a_{47}=-11+(-138)$

STEP 6

Finally, perform the addition to find the47th term.
$a_{47}=-11-138=-149$ So, the47th term of the arithmetic sequence is -149.
The correct answer is A. -149.

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.

QuestionFind the 47th term of the sequence given by an=−11+(n−1)(−3)a_{n}=-11+(n-1)(-3)an​=−11+(n−1)(−3). Options: A. -149 B. -152 C. 127 D. -138

Studdy Solution

STEP 1

Assumptions1. The explicit formula for the arithmetic sequence is an=−11+(n−1)(−3)a_{n}=-11+(n-1)(-3)an​=−11+(n−1)(−3). We are looking for the47th term of the sequence, i.e., n=47n=47n=47

STEP 2

STEP 3

We can see that the first term a1a_{1}a1​ is -11 and the common difference ddd is -3. We are asked to find the47th term, so we substitute n=47n=47n=47 into the formula.a47=−11+(47−1)(−3)a_{47}=-11+(47-1)(-3)a47​=−11+(47−1)(−3)

STEP 4

First, simplify the expression inside the parentheses.a47=−11+(46)(−3)a_{47}=-11+(46)(-3)a47​=−11+(46)(−3)

STEP 5

Next, perform the multiplication.a47=−11+(−138)a_{47}=-11+(-138)a47​=−11+(−138)

STEP 6

Finally, perform the addition to find the47th term.a47=−11−138=−149a_{47}=-11-138=-149a47​=−11−138=−149So, the47th term of the arithmetic sequence is -149.The correct answer is A. -149.

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.

QuestionFind the 47th term of the sequence given by $a_{n}=-11+(n-1)(-3)$ . Options: A. -149 B. -152 C. 127 D. -138

Assumptions1. The explicit formula for the arithmetic sequence is $a_{n}=-11+(n-1)(-3)$ . We are looking for the47th term of the sequence, i.e., $n=47$

We can see that the first term $a_{1}$ is -11 and the common difference $d$ is -3. We are asked to find the47th term, so we substitute $n=47$ into the formula.
$a_{47}=-11+(47-1)(-3)$

First, simplify the expression inside the parentheses.
$a_{47}=-11+(46)(-3)$

Next, perform the multiplication.
$a_{47}=-11+(-138)$

Finally, perform the addition to find the47th term.
$a_{47}=-11-138=-149$ So, the47th term of the arithmetic sequence is -149.
The correct answer is A. -149.