This is the first 5 terms of a sequence

−
1
,
2
,
5
,
8
,
11
−1,2,5,8,11
What is the nth term of this sequence?

The given sequence is: \(-1, 2, 5, 8, 11\).

We can observe that the terms follow a pattern of adding 3 to each consecutive term:

\[
2 - (-1) = 3, \quad 5 - 2 = 3, \quad 8 - 5 = 3, \quad 11 - 8 = 3.
\]

Thus, the sequence has a common difference of 3, indicating that it is an **arithmetic sequence**.

The general formula for the \(n\)-th term of an arithmetic sequence is:

\[
a_n = a_1 + (n-1) \cdot d
\]

Where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term of the sequence (\(-1\) in this case),
- \(d\) is the common difference (\(3\) in this case),
- \(n\) is the position of the term in the sequence.

Substituting the known values into the formula:

\[
a_n = -1 + (n-1) \cdot 3
\]
\[
a_n = -1 + 3n - 3
\]
\[
a_n = 3n - 4
\]

Thus, the \(n\)-th term of the sequence is:

\[
a_n = 3n - 4
\]

### Do you want further details or have any questions?

### 5 Related Questions:
1. How do you find the common difference in an arithmetic sequence?
2. Can you derive the general form for any arithmetic sequence?
3. What is the sum of the first \(n\) terms of this sequence?
4. How do you identify an arithmetic sequence from a set of numbers?
5. What happens to the \(n\)-th term formula if the common difference is negative?

### Tip:
In an arithmetic sequence, the common difference remains constant, which is key to finding both the general term and the sum formula.

This is the first 5 terms of a sequence -1, 2, 5, 8, 11. What is the nth term of this sequence?

Discover how to find the nth term of the arithmetic sequence -1, 2, 5, 8, 11 using a detailed step-by-step solution. This problem demonstrates key algebraic concepts, including arithmetic sequences and the formula for the nth term. Ideal for Grades 7-9 students.

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