Find a formula for the $$ n $$th term of the arithmetic sequence. First term - 12 Common difference 4 $$ a_{n}=[?] n+[\quad] $$

Question

UpStudy AI · Accepted Answer

To find the $$ n $$th term of an arithmetic sequence, you can use the formula:

$$
a_n = a_1 + (n - 1)d
$$

where:
- $$ a_1 $$ is the first term,
- $$ d $$ is the common difference,
- $$ n $$ is the term number.

Given:
- First term ($$ a_1 $$) = 12
- Common difference ($$ d $$) = 4

Plugging these values into the formula:

$$
a_n = 12 + (n - 1) \times 4
$$
$$
a_n = 12 + 4n - 4
$$
$$
a_n = 4n + 8
$$

So, the formula for the $$ n $$th term is:

$$
a_{n} = 4n + 8
$$

**Answer:** 
$$
a_{n} = 4\,n\;+\;8
$$
The $$ n $$th term of the arithmetic sequence is $$ a_{n} = 4n + 8 $$.

Find a formula for the \( n \)th term of the arithmetic sequence. First term - 12 Common difference 4 \( a_{n}=[?] n+[\quad] \)