You provided a sequence defined by the following recurrence relation:

- \( a_1 = 3 \)
- \( a_n = a_{n-1} + 11 \)

This is an arithmetic sequence because each term after the first is generated by adding a constant difference (11 in this case) to the previous term.

### General Form of the Sequence

For an arithmetic sequence, the \(n\)th term can be expressed as:

\[
a_n = a_1 + (n-1) \times d
\]

Where:
- \( a_1 \) is the first term.
- \( d \) is the common difference.
- \( n \) is the term number.

### Applying the Values

Here, \( a_1 = 3 \) and \( d = 11 \), so:

\[
a_n = 3 + (n-1) \times 11
\]

Simplifying the equation:

\[
a_n = 3 + 11n - 11
\]
\[
a_n = 11n - 8
\]

So, the general form of the sequence is:

\[
\boxed{a_n = 11n - 8}
\]

### Example Calculation
To find specific terms:
- \( a_2 = 11(2) - 8 = 22 - 8 = 14 \)
- \( a_3 = 11(3) - 8 = 33 - 8 = 25 \)

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find the sum of the first \(n\) terms in an arithmetic sequence?
2. What are the properties of an arithmetic sequence?
3. How would you solve for the term number \(n\) given \(a_n\)?
4. Can you derive the formula for the general term of a geometric sequence?
5. How do arithmetic sequences differ from geometric sequences?

**Tip:** Always double-check the common difference to ensure it's consistent throughout the sequence when dealing with arithmetic sequences.

Explore the arithmetic sequence defined by the recurrence relation a1 = 3, an = an-1 + 11. Learn how to derive the nth term formula and calculate specific terms. Suitable for Grades 7-9.

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