This is an arithmetic sequence where:

• First term: $a_1 = 12$
• Common difference: $d = 19 - 12 = 7$

The explicit formula for an arithmetic sequence is:

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

Substituting the values:

$a_n = 12 + (n - 1) \cdot 7$

$a_n = 12 + 7n - 7$

$a_n = 7n + 5$

Thus, the explicit formula is:

$a_n = 7n + 5$

Would you like a step-by-step breakdown or additional examples?

Related Questions:

1. How do you find the sum of the first $n$ terms of an arithmetic sequence?
2. How do you determine whether a sequence is arithmetic or geometric?
3. What is the recursive formula for this sequence?
4. If the 10th term is given, how can you find the first term?
5. How does changing the common difference affect the sequence?

Tip:

Always check the pattern in an arithmetic sequence by verifying that the difference between consecutive terms is constant.