Understanding the Common Difference in Arithmetic Sequences: Definition, Calculation, and Importance

Common Difference

In mathematics, the term “common difference” is often associated with arithmetic sequences

In mathematics, the term “common difference” is often associated with arithmetic sequences. An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is a constant value.

The common difference (d) is the fixed value that is added or subtracted from each term in an arithmetic sequence to obtain the next term. For example, consider the arithmetic sequence: 1, 4, 7, 10, 13, …

To find the common difference in this sequence, we can subtract each term from its consecutive term:
4 – 1 = 3
7 – 4 = 3
10 – 7 = 3
13 – 10 = 3
…

As we can see, the difference between any two consecutive terms is always 3. Therefore, the common difference in this sequence is 3.

The common difference can be positive, negative, or zero. If the common difference is positive, the terms in the sequence will increase as we move forward. If the common difference is negative, the terms will decrease. And if the common difference is zero, all terms in the sequence will be the same.

The common difference is an important concept in arithmetic sequences as it allows us to easily find any term in the sequence using the formula:

a_n = a_1 + (n – 1)d

Where a_n is the nth term of the sequence, a_1 is the first term, n is the position number of the term, and d is the common difference.

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