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The problem provides the following information about an arithmetic sequence:

- First term (\(a_1\)) = \(-26\)
- 85th term (\(a_{85}\)) = \(-362\)

We are asked to find the value of the 35th term (\(a_{35}\)).

### Formula for an arithmetic sequence:
The general formula for the \(n\)-th term of an arithmetic sequence is:
\[
a_n = a_1 + (n - 1) \cdot d
\]
Where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term,
- \(d\) is the common difference between consecutive terms,
- \(n\) is the term number.

### Step 1: Use the formula to find the common difference \(d\)
We know the first term (\(a_1 = -26\)) and the 85th term (\(a_{85} = -362\)). Plugging these into the formula:

\[
a_{85} = a_1 + (85 - 1) \cdot d
\]
\[
-362 = -26 + 84 \cdot d
\]
Now, solve for \(d\):

\[
-362 + 26 = 84 \cdot d
\]
\[
-336 = 84 \cdot d
\]
\[
d = \frac{-336}{84} = -4
\]

### Step 2: Find the 35th term
Now that we know the common difference \(d = -4\), we can find the 35th term using the formula:

\[
a_{35} = a_1 + (35 - 1) \cdot d
\]
\[
a_{35} = -26 + 34 \cdot (-4)
\]
\[
a_{35} = -26 - 136
\]
\[
a_{35} = -162
\]

### Final Answer:
The value of the 35th term (\(a_{35}\)) is \(-162\).

Would you like more details on any part of this solution, or do you have any additional questions?

Here are some related questions you might find helpful:
1. How do you derive the formula for the \(n\)-th term of an arithmetic sequence?
2. How can the sum of the first \(n\) terms of an arithmetic sequence be calculated?
3. What is the difference between arithmetic and geometric sequences?
4. How can we determine if a sequence is arithmetic or not?
5. Can you solve an arithmetic sequence problem using a graph?

**Tip:** In arithmetic sequences, the common difference \(d\) remains constant between any two consecutive terms.

Dada una sucesión aritmética, el primer término, a₁, es igual a -26, y el 85º término, a₈₅, es igual a -362. Hallar el valor del 35º término, a₃₅.

Solve an arithmetic sequence problem where the first term a₁ is -26, the 85th term a₈₅ is -362, and we are tasked with finding the 35th term a₃₅. Learn how to use the formula aₙ = a₁ + (n - 1) * d to find the common difference and calculate the required term.

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