To solve this problem and write an equation for the sequence, we follow these steps:

Step 1: Identify the pattern in the sequence.

The sequence is:
$-61, \, -122, \, -244, \, \dots$
We calculate the common difference, $d$, between consecutive terms:
$d = -122 - (-61) = -122 + 61 = -61$
$d = -244 - (-122) = -244 + 122 = -122$
Thus, the common difference $d$ is $-61$.

Step 2: Use the formula for an arithmetic sequence.

The general form for an arithmetic sequence is:
$a_n = a_1 + (n-1)d$
where:

• $a_n$ is the $n$-th term,
• $a_1$ is the first term,
• $d$ is the common difference,
• $n$ is the position of the term.

Step 3: Substitute the known values.

• $a_1 = -61$ (first term)
• $d = -61$ (common difference)

Substitute into the formula:
$a_n = -61 + (n-1)(-61)$

Simplify:
$a_n = -61 - 61(n-1)$

Distribute $-61$:
$a_n = -61 - 61n + 61$

Combine like terms:
$a_n = -61n$

Final Answer:

The equation for the sequence is:
$a_n = -61n$

If you have further questions or need a more detailed explanation, let me know!

Related Questions:

1. What is the general formula for an arithmetic sequence?
2. How do you find the common difference in a sequence?
3. What would be the 5th term of this sequence?
4. Can you determine the $n$-th term for a geometric sequence instead?
5. How would you write the sequence if the common difference was positive?

Tip: Always check for the common difference first in any sequence to confirm if it is arithmetic.