To determine the explicit formula for an arithmetic sequence, you need two key pieces of information:

1. The first term of the sequence, $a_1$.
2. The common difference between consecutive terms, $d$.

Given the general form $a_n = a_1 + d(n − 1)$, let's define how to find each element:

• $a_1$ is simply the first term of the sequence.
• $d$ is the common difference, which you find by subtracting any term from the previous term in the sequence.

Example:

If you are given a sequence like 3, 7, 11, 15,...

1. Identify $a_1$: The first term is 3.
2. Determine $d$: The difference between each term is $7 - 3 = 4$.

So, the explicit formula for this sequence would be: $a_n = 3 + 4(n − 1)$

Which can be simplified to: $a_n = 4n - 1$

Would you like to provide a specific sequence for a more detailed explanation?

---

Relative Questions:

1. How do you calculate the common difference in an arithmetic sequence?
2. What happens to the explicit formula if the common difference is negative?
3. Can the first term $a_1$ be zero in an arithmetic sequence?
4. How do you find the $n$-th term if only the first few terms are given?
5. What is the impact on the sequence if the common difference $d$ changes after a certain term?

Tip: Always check the consistency of the common difference across the sequence to confirm it's arithmetic.