To solve the problem, let's define the variables:

- \( t_1 \) = first term
- \( t_2 \) = second term
- \( t_3 \) = third term

Given the equations:
1. \( t_1 + t_2 = 18 \)
2. \( t_2 + t_3 = 36 \)

### Step 1: Express \( t_3 \) in terms of \( t_1 \)
From the second equation:
\[
t_3 = 36 - t_2
\]

### Step 2: Express \( t_1 \) in terms of \( t_3 \)
Substitute \( t_2 \) from the first equation:
\[
t_2 = 18 - t_1
\]

Substituting this into the expression for \( t_3 \):
\[
t_3 = 36 - (18 - t_1) = 18 + t_1
\]

### Step 3: Solve for \( t_1 \)
From the expression for \( t_3 \) and \( t_1 + t_2 = 18 \), we can deduce the following:
\[
t_1 + (36 - t_3) = 18
\]
Given that \( t_3 = 18 + t_1 \), substitute this into the equation above:
\[
t_1 + (36 - (18 + t_1)) = 18
\]

Simplifying this:
\[
t_1 + 18 - t_1 = 18
\]

This means the equation holds true, indicating that \( t_1 \) and \( t_2 \) must be solved with another relationship. 

### Step 4: Find the difference \( d_r \)
If the sequence were arithmetic (assuming the problem implicitly suggests this), the common difference \( d_r \) would be the same across the sequence. Using the fact that \( t_2 = 18 - t_1 \) and \( t_3 = 18 + t_1 \), we can deduce:
\[
d_r = t_2 - t_1 = t_3 - t_2
\]
This leads to:
\[
d_r = (36 - t_3) - t_1
\]

To obtain a specific solution, we need additional constraints or specifics about the relationship between the terms.

Would you like further details on this problem, or do you have specific assumptions in mind that I should consider? Here are some related questions to explore:

1. How would the solution change if this sequence is arithmetic?
2. What if the sequence was geometric? How would you approach the problem?
3. Can you find the general formula for the \( n \)-th term if you had a specific pattern?
4. What are possible values of \( t_1 \) and \( t_2 \) if the terms are in a linear sequence?
5. How do the sum of terms \( t_1 + t_2 + t_3 \) compare under different conditions?

**Tip:** Always verify if additional assumptions or conditions exist when solving sequence-related problems.

Learn how to solve linear equations within arithmetic sequences using the given conditions. Explore the relationship between terms and find the common difference. Suitable for high school students.

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