Math Problem Statement

Which of the following describes an arithmetic sequence? A. A sequence in which the sum of any two consecutive terms is a constant B. A sequence in which the difference between any two consecutive terms is a constant C. A sequence in which the product of any two consecutive terms is a constant D. A sequence in which the quotient of any two consecutive terms is a constant

Solution

The correct answer to the question is:

B. A sequence in which the difference between any two consecutive terms is a constant.

Explanation:

An arithmetic sequence is defined as a sequence where the difference between any two consecutive terms is constant. This constant is called the "common difference," denoted as dd.

For example:

  • In the sequence 2,5,8,11,2, 5, 8, 11, \ldots, the difference between consecutive terms is 52=35 - 2 = 3, 85=38 - 5 = 3, etc., so the common difference d=3d = 3.

Let me know if you'd like additional explanations or examples!


Related Questions:

  1. How can you find the nn-th term of an arithmetic sequence?
  2. What is the formula for the sum of the first nn terms of an arithmetic sequence?
  3. How do arithmetic sequences differ from geometric sequences?
  4. Can an arithmetic sequence have a common difference of zero? What does that mean?
  5. What are real-life examples of arithmetic sequences?

Tip: When identifying sequences, remember to carefully check for consistent changes (difference, ratio, etc.) to classify the type of sequence.

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Math Problem Analysis

Mathematical Concepts

Sequences
Arithmetic Sequence
Common Difference

Formulas

nth term formula for an arithmetic sequence: a_n = a_1 + (n-1)d

Theorems

Definition of Arithmetic Sequence

Suitable Grade Level

Grades 7-9