To find the explicit formula for the nth term of an arithmetic sequence, we use the general form:

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

Where:

• $a_1$ is the first term,
• $d$ is the common difference between consecutive terms,
• $n$ is the term number.

For the given sequence: 3, 10, 17, 24, ...

• The first term $a_1 = 3$,
• The common difference $d = 10 - 3 = 7$.

Now, substitute these values into the formula:

$a_n = 3 + (n - 1) \cdot 7$

Simplify the expression:

$a_n = 3 + 7n - 7$ $a_n = 7n - 4$

Thus, the explicit formula for the nth term is:

$a_n = 7n - 4$

Would you like more details on how to derive the formula, or do you have any questions?

---

Here are 5 related questions to explore further:

1. How do you find the common difference in an arithmetic sequence?
2. What is the formula for the sum of the first n terms in an arithmetic sequence?
3. How does an arithmetic sequence differ from a geometric sequence?
4. What happens if the common difference is negative in an arithmetic sequence?
5. Can you find the 10th term using the explicit formula?

Tip: Always verify the formula by checking if it gives the correct result for a few terms from the sequence.