To solve this problem:

We need to find the 8th term of an arithmetic sequence where:

• The first term $a_1 = 3x + y$,
• The common difference $d = x + y$.

Formula for the $n$-th term of an arithmetic sequence:

$a_n = a_1 + (n-1) \cdot d$

Step-by-step solution:

1. Substitute the known values into the formula: $a_8 = a_1 + (8-1) \cdot d$

2. Simplify: $a_8 = (3x + y) + 7 \cdot (x + y)$

3. Distribute $7$ to $(x + y)$: $a_8 = 3x + y + 7x + 7y$

4. Combine like terms: $a_8 = (3x + 7x) + (y + 7y)$ $a_8 = 10x + 8y$

Final Answer:

The 8th term of the sequence is: $\boxed{10x + 8y}$

This matches the second option in the multiple-choice answers. Let me know if you need further clarification!

Related Questions to Expand Learning:

1. How would you find the 10th term of this arithmetic sequence?
2. What would the common difference need to be for the 8th term to equal $20x + 16y$?
3. How do you write the general formula for the $n$-th term in this sequence?
4. How does this sequence behave if $x = y$?
5. Can you graph the arithmetic sequence for visual understanding?

Tip:

Always write out and simplify the formula step by step to ensure accuracy in arithmetic sequences.