Find the 69th term of the arithmetic sequence minus, 13, comma, minus, 33, comma, minus, 53, comma, point, point, .−13,−33,−53

To find the 69th term of the arithmetic sequence \(-13, -33, -53, \dots\), follow these steps:

1. **Identify the first term (\(a_1\))**: The first term is \(a_1 = -13\).

2. **Determine the common difference (\(d\))**: The common difference is calculated by subtracting the first term from the second term:
   \[
   d = -33 - (-13) = -33 + 13 = -20
   \]

3. **Use the formula for the \(n\)th term of an arithmetic sequence**:
   \[
   a_n = a_1 + (n - 1) \cdot d
   \]

4. **Substitute the values to find the 69th term**:
   \[
   a_{69} = -13 + (69 - 1) \cdot (-20)
   \]
   \[
   a_{69} = -13 + 68 \cdot (-20)
   \]
   \[
   a_{69} = -13 - 1360
   \]
   \[
   a_{69} = -1373
   \]

So, the 69th term of the sequence is \(-1373\).

Would you like more details or have any questions?

Here are some related questions:
1. How do you find the sum of the first 69 terms of this arithmetic sequence?
2. What is the 100th term of this sequence?
3. Can you derive the general formula for the \(n\)th term of this sequence?
4. How would the sequence change if the common difference was positive?
5. How can you find the middle term of an arithmetic sequence?

**Tip:** When dealing with negative common differences, the terms in the sequence will decrease steadily.

Discover how to find the 69th term of the arithmetic sequence -13, -33, -53, and more. Follow our step-by-step solution using the arithmetic sequence nth term formula. Suitable for students in Grades 9-12.

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