Math Problem Statement

-11,-17,-23 common difference

Solution

To find the common difference of an arithmetic sequence, subtract any term from the term that follows it.

In your sequence, the terms are:
11,17,23-11, -17, -23.

Let's calculate the common difference:

d=17(11)=17+11=6d = -17 - (-11) = -17 + 11 = -6

Next, check the difference between the second and third terms:

d=23(17)=23+17=6d = -23 - (-17) = -23 + 17 = -6

Thus, the common difference dd is 6-6.

Would you like to explore more details or have any questions?

Here are 5 related questions to expand your understanding:

  1. How do you find the nn-th term of an arithmetic sequence?
  2. What is the sum of the first nn terms of an arithmetic sequence?
  3. How do you determine if a sequence is arithmetic?
  4. How does changing the common difference affect the sequence?
  5. How can you graph an arithmetic sequence?

Tip: The formula for the nn-th term of an arithmetic sequence is an=a1+(n1)da_n = a_1 + (n-1) \cdot d.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Algebra

Formulas

d = a_n - a_(n-1)
a_n = a_1 + (n-1) * d

Theorems

Arithmetic Sequence Formula

Suitable Grade Level

Grades 6-8