An arithmetic sequence is given below.

3

,  

10

,  

17

,  

24

,  

...

Write an explicit formula for the 

*n*th

 term 

*an*

.


=*an*

To find the explicit formula for the *n*th 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 *n*th 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.

An arithmetic sequence is given below.
3, 10, 17, 24, ...
Write an explicit formula for the nth term an.

Learn how to find the explicit formula for the nth term of an arithmetic sequence. This example covers the sequence 3, 10, 17, 24, and uses the general form an = a1 + (n - 1) * d. Perfect for students in Grades 6-8.

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