The problem asks to find the 30th term ($a_{30}$) of the arithmetic sequence: $2, 0, -2, -4, -6, \dots$.

In an arithmetic sequence, the general formula for the $n$-th term ($a_n$) is given by:

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

Where:

• $a_1$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

Step 1: Identify the values

• $a_1 = 2$ (the first term of the sequence),
• $d = 0 - 2 = -2$ (the common difference between consecutive terms).

Step 2: Apply the formula

We want to find the 30th term, so: $a_{30} = a_1 + (30 - 1) \cdot d$ $a_{30} = 2 + (30 - 1) \cdot (-2)$ $a_{30} = 2 + 29 \cdot (-2)$ $a_{30} = 2 - 58$ $a_{30} = -56$

Thus, the 30th term is $-56$, so the correct answer is c. -56.

Would you like more details or have any other questions?

Here are 5 related questions you might find useful:

1. What is the formula for the sum of an arithmetic series?
2. How do you find the common difference in an arithmetic progression?
3. How do you determine the general term of a geometric sequence?
4. What is the difference between arithmetic and geometric progressions?
5. How can you use arithmetic sequences to solve real-life problems?

Tip: When solving for any term in an arithmetic sequence, always ensure to correctly identify both the first term and the common difference, as they are crucial for accurate calculations.