QuestionFind a formula for $a_{n}$ based on the sequence: -4, 9, -14, 19, -24. What is $a_{n}=$ ?

Studdy Solution

STEP 1

Assumptions1. The sequence given is $-4,9, -14,19, -24, \ldots$ . The sequence starts from $a0$ and continues as $a1, a, a3, \ldots$
3. We need to find a general formula $a_n$ for the nth term of the sequence.

STEP 2

First, let's observe the pattern in the sequence. The sequence alternates between negative and positive values. Also, the absolute value of the terms increases by5 each time.

STEP 3

Let's write down the sequence along with their term numbers.
Term number0,1,2,3,, ... Corresponding term -,9, -14,19, -24, ...

STEP 4

We can see that the absolute value of the nth term is4 more than times the term number.
$|a_n| =n +4$

STEP 5

Now, we need to account for the alternating sign. We can do this by multiplying the absolute value by $(-1)^n$ .
$a_n = (-1)^n (5n +4)$ This formula will give us the nth term of the sequence.

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QuestionFind a formula for $a_{n}$ based on the sequence: -4, 9, -14, 19, -24. What is $a_{n}=$ ?

Studdy Solution

STEP 1

Assumptions1. The sequence given is $-4,9, -14,19, -24, \ldots$ . The sequence starts from $a0$ and continues as $a1, a, a3, \ldots$
3. We need to find a general formula $a_n$ for the nth term of the sequence.

STEP 2

First, let's observe the pattern in the sequence. The sequence alternates between negative and positive values. Also, the absolute value of the terms increases by5 each time.

STEP 3

Let's write down the sequence along with their term numbers.
Term number0,1,2,3,, ... Corresponding term -,9, -14,19, -24, ...

STEP 4

We can see that the absolute value of the nth term is4 more than times the term number.
$|a_n| =n +4$

STEP 5

Now, we need to account for the alternating sign. We can do this by multiplying the absolute value by $(-1)^n$ .
$a_n = (-1)^n (5n +4)$ This formula will give us the nth term of the sequence.

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QuestionFind a formula for ana_{n}an​ based on the sequence: -4, 9, -14, 19, -24. What is an=a_{n}=an​=?

Studdy Solution

STEP 1

Assumptions1. The sequence given is −4,9,−14,19,−24,…-4,9, -14,19, -24, \ldots−4,9,−14,19,−24,… . The sequence starts from a0a0a0 and continues as a1,a,a3,…a1, a, a3, \ldotsa1,a,a3,…3. We need to find a general formula ana_nan​ for the nth term of the sequence.

STEP 2

First, let's observe the pattern in the sequence. The sequence alternates between negative and positive values. Also, the absolute value of the terms increases by5 each time.

STEP 3

Let's write down the sequence along with their term numbers.Term number0,1,2,3,, ... Corresponding term -,9, -14,19, -24, ...

STEP 4

We can see that the absolute value of the nth term is4 more than times the term number.∣an∣=n+4|a_n| =n +4∣an​∣=n+4

STEP 5

Now, we need to account for the alternating sign. We can do this by multiplying the absolute value by (−1)n(-1)^n(−1)n.an=(−1)n(5n+4)a_n = (-1)^n (5n +4)an​=(−1)n(5n+4)This formula will give us the nth term of the sequence.

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Studdy solves anything!

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QuestionFind a formula for $a_{n}$ based on the sequence: -4, 9, -14, 19, -24. What is $a_{n}=$ ?

Assumptions1. The sequence given is $-4,9, -14,19, -24, \ldots$ . The sequence starts from $a0$ and continues as $a1, a, a3, \ldots$
3. We need to find a general formula $a_n$ for the nth term of the sequence.

Let's write down the sequence along with their term numbers.
Term number0,1,2,3,, ... Corresponding term -,9, -14,19, -24, ...

We can see that the absolute value of the nth term is4 more than times the term number.
$|a_n| =n +4$

Now, we need to account for the alternating sign. We can do this by multiplying the absolute value by $(-1)^n$ .
$a_n = (-1)^n (5n +4)$ This formula will give us the nth term of the sequence.