6. The common difference = d in an Arithmetic Sequence is the... (A) the sum of any two consecutive terms (B) the product of any two consecutive terms (C) the consistent change in value between any two consecutive terms (D) the consistent ratio of any two consecutive terms
Answer (1)
In an Arithmetic Sequence, the common difference, denoted as d , is defined as the consistent change in value between any two consecutive terms. This is a fundamental property of an arithmetic sequence.
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This constant difference is what we call the 'common difference'. For example, in the sequence 3, 6, 9, 12, 15, the common difference d is 3.
To determine the common difference, you subtract any term from the subsequent term. Mathematically, if we denote the terms of the sequence as a 1 , a 2 , a 3 , … , the common difference d can be expressed as:
d = a n + 1 − a n
where a n is any term in the sequence, and a n + 1 is the term that directly follows.
Therefore, the correct choice for the definition of the common difference in an arithmetic sequence is (C) the consistent change in value between any two consecutive terms.
