Find the 88th term of the arithmetic sequence 4, comma, minus, 1, comma, minus, 6, comma, point, point, .4,−1,−6

To find the 88th term of the arithmetic sequence, we first need to identify the first term \(a_1\) and the common difference \(d\).

Given the sequence: \(4, -1, -6, \dots\)

1. **First term (\(a_1\))**: The first term is \(a_1 = 4\).

2. **Common difference (\(d\))**: The common difference is calculated by subtracting the first term from the second term:
   \[
   d = -1 - 4 = -5
   \]

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

4. **Substitute the values to find the 88th term**:
   \[
   a_{88} = 4 + (88 - 1) \cdot (-5)
   \]
   \[
   a_{88} = 4 + 87 \cdot (-5)
   \]
   \[
   a_{88} = 4 - 435
   \]
   \[
   a_{88} = -431
   \]

So, the 88th term of the sequence is \(-431\).

Would you like more details or have any questions?

Here are some related questions:
1. How do you find the sum of the first 88 terms of this arithmetic sequence?
2. What is the 100th term of this sequence?
3. How can you derive the formula for the \(n\)th term of an arithmetic sequence?
4. What is the common difference if the sequence were \(5, -2, -9, \dots\)?
5. How do you determine whether a sequence is arithmetic or not?

**Tip:** In an arithmetic sequence, each term is found by adding the common difference to the previous term.

Learn how to find the 88th term of the arithmetic sequence 4, -1, -6 with a step-by-step solution. This problem covers arithmetic sequences, including the formula for the nth term. Suitable for Grade 7 students.

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