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 .
For example:
- In the sequence , the difference between consecutive terms is , , etc., so the common difference .
Let me know if you'd like additional explanations or examples!
Related Questions:
- How can you find the -th term of an arithmetic sequence?
- What is the formula for the sum of the first terms of an arithmetic sequence?
- How do arithmetic sequences differ from geometric sequences?
- Can an arithmetic sequence have a common difference of zero? What does that mean?
- 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