Find the 60th term of the arithmetic sequence minus, 14, comma, minus, 25, comma, minus, 36, comma, point, point, .−14,−25,−36

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.

Find the 60th term of the arithmetic sequence: -14, -25, -36, ...

Learn how to find the 60th term of the arithmetic sequence -14, -25, -36, ... using the arithmetic sequence formula. This step-by-step solution is suitable for students in Grades 8-10 and covers key algebra concepts like common difference and nth term calculations.

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