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: 
\[
-1, 2, 5, 8, 11
\]

This appears to be an arithmetic sequence, where each term increases by a constant difference. Let's calculate the common difference:

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

So, the common difference \(d = 3\).

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

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

Where:
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.

For this sequence:
- \(a_1 = -1\),
- \(d = 3\).

Substituting these 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:

\[
a_n = 3n - 4
\]

Would you like further details on this, or do you have any questions?

Here are 5 questions related to arithmetic sequences:
1. How do you find the sum of the first \(n\) terms of an arithmetic sequence?
2. How does the formula for the \(n\)-th term change if the common difference is negative?
3. Can you apply this formula to find the 10th term of the sequence?
4. What is the general condition for a sequence to be arithmetic?
5. How would you find the common difference if the terms were given as algebraic expressions?

**Tip:** In arithmetic sequences, the difference between consecutive terms is always constant. This can help quickly identify such sequences.

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. This solution breaks down the process of identifying the common difference and using the arithmetic sequence formula to calculate any term. Suitable for Grades 6-8.

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