In an arithmetic sequence, the difference between consecutive terms is constant. The formula to find the $n$-th term of 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, and
• $n$ is the term number.

Step 1: Identify the values

From the given sequence: $-14, -25, -36, \dots$,

• $a_1 = -14$ (the first term),
• $d = -25 - (-14) = -25 + 14 = -11$ (the common difference).

Step 2: Use the formula

To find the 60th term ($a_{60}$): $a_{60} = a_1 + (60 - 1)d$ $a_{60} = -14 + (59)(-11)$ $a_{60} = -14 - 649$ $a_{60} = -663$

So, the 60th term of the sequence is $-663$.

Would you like further clarification or additional details?

Here are 5 related questions to explore:

1. How do you determine the common difference in an arithmetic sequence?
2. What is the formula for the sum of the first $n$ terms of an arithmetic sequence?
3. How does an arithmetic sequence differ from a geometric sequence?
4. How can you determine if a sequence is arithmetic?
5. What happens to the sequence if the common difference is positive?

Tip: The common difference in an arithmetic sequence determines how the terms grow or shrink—positive values increase the sequence, while negative values decrease it.