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To solve for \( n \) from the equation provided:

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

It seems that the equation contains a mistake because \( a_n \) is on both sides, which leads to a trivial identity. There might be a typo or misinterpretation. 

If we assume the equation should be something like:

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

This would correspond to the formula for the \( n \)-th term of an arithmetic sequence, where:
- \( a_1 \) is the first term,
- \( d \) is the common difference,
- \( a_n \) is the \( n \)-th term.

Now, to solve for \( n \):

1. Rearrange the equation:
\[
a_n = a_1 + d(n - 1)
\]

2. Subtract \( a_1 \) from both sides:
\[
a_n - a_1 = d(n - 1)
\]

3. Divide both sides by \( d \):
\[
\frac{a_n - a_1}{d} = n - 1
\]

4. Add 1 to both sides to isolate \( n \):
\[
n = \frac{a_n - a_1}{d} + 1
\]

Thus, \( n \) is given by:
\[
n = \frac{a_n - a_1}{d} + 1
\]

Let me know if this helps or if you need further clarification!

### Here are 5 related questions for further exploration:
1. What is an arithmetic sequence, and how is it different from a geometric sequence?
2. How would you find the sum of the first \( n \) terms of an arithmetic sequence?
3. What happens when the common difference \( d \) in an arithmetic sequence is negative?
4. Can this formula be applied to find the position of any term in the sequence?
5. How does this formula change if the sequence starts at a different index?

### Tip:
When solving for a variable, carefully rearrange the terms step-by-step, keeping track of all operations performed on each side of the equation to avoid mistakes.

Learn how to solve for n in the arithmetic sequence formula a_n = a_1 + d(n - 1). This step-by-step guide explains the algebraic rearrangement and helps you understand sequences. Ideal for high school students.

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