Math Problem Statement

Find the common difference of the arithmetic sequence 19, comma, 27, comma, 35, comma, point, point, .19,27,35,...

Solution

The common difference in an arithmetic sequence is found by subtracting any term from the term that follows it.

In the given sequence: 19,27,35,19, 27, 35, \dots

Let's subtract the first term from the second term: d=2719=8d = 27 - 19 = 8

Now, let's verify by subtracting the second term from the third term: d=3527=8d = 35 - 27 = 8

Since the difference between consecutive terms is the same, the common difference is 8\mathbf{8}.

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

Here are 5 related questions:

  1. What is the next term in this arithmetic sequence?
  2. How can you find the nn-th term of this arithmetic sequence?
  3. What is the sum of the first 10 terms of this arithmetic sequence?
  4. How does an arithmetic sequence differ from a geometric sequence?
  5. What are some real-world examples of arithmetic sequences?

Tip: In an arithmetic sequence, you can always check the common difference by subtracting any term from the next!

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Algebra

Formulas

Common difference formula: d = a(n+1) - a(n)

Theorems

Arithmetic sequence formula

Suitable Grade Level

Grades 6-8