In an arithmetic sequence, each term differs from the previous one by a constant amount called the common difference. This characteristic allows us to express the sequence in terms of a linear function.

To determine the linear function for this arithmetic sequence, let’s denote:

• The initial value $a_0$ (when $n = 0$),
• The common difference $d$, which is the amount added to each term to obtain the next term.

The formula for the general term of an arithmetic sequence is: $a_n = a_0 + n \cdot d$

Here:

• $a_0$ is the value of the sequence when $n = 0$,
• $n$ is the term number, and
• $d$ is the common difference.

Steps to Determine the Linear Function:

1. Identify $a_0$: Use the value of the sequence at $n = 0$.
2. Determine $d$: Calculate the difference between consecutive terms.
3. Construct the Function: Substitute $a_0$ and $d$ into the formula $a_n = a_0 + n \cdot d$.

If you have specific values in the table for selected terms $a_n$, we can calculate $d$ and $a_0$ directly.

Would you like to provide the table so I can proceed with constructing the exact function? Or do you have any specific questions on these steps?

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Here are five related questions for further understanding:

1. What if the common difference is negative? How does it affect the sequence?
2. How can we determine the value of $n$ for any given term in an arithmetic sequence?
3. How do we identify if a given sequence is arithmetic just by looking at a table of values?
4. What if the sequence started from $n = 1$ instead of $n = 0$? How would the formula change?
5. How can we apply arithmetic sequences to solve real-world problems?

Tip: In arithmetic sequences, checking a few consecutive terms for a constant difference quickly reveals whether it is indeed arithmetic.