https://r2.erweima.ai/mathbot/image/1725543780672mx72c43b.jpg

The problem in the image asks to **find the common difference of the arithmetic sequence: -1, 8, 17, ...**

In an arithmetic sequence, the common difference \(d\) is the constant value added to each term to get the next term. The formula to find the common difference between consecutive terms is:

\[
d = a_{n+1} - a_n
\]

Using the given sequence:

- First term (\(a_1\)) = -1
- Second term (\(a_2\)) = 8
- Third term (\(a_3\)) = 17

We calculate the difference:

\[
d = a_2 - a_1 = 8 - (-1) = 8 + 1 = 9
\]
\[
d = a_3 - a_2 = 17 - 8 = 9
\]

Thus, the **common difference** is \( \mathbf{9} \).

Would you like further explanation or details?

### Related Questions:
1. How do you find the nth term of an arithmetic sequence?
2. Can an arithmetic sequence have a negative common difference?
3. How can the sum of the first n terms in an arithmetic sequence be calculated?
4. What is the formula for the general term of an arithmetic sequence?
5. How does an arithmetic sequence differ from a geometric sequence?

### Tip:
To confirm the common difference, always subtract any consecutive terms of the sequence.

Find the common difference of the arithmetic sequence: -1, 8, 17, ...

Learn how to find the common difference in an arithmetic sequence using the example: -1, 8, 17. This problem demonstrates the use of algebraic formulas to determine the common difference between consecutive terms, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation