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

Common Difference d

In mathematics, the common difference (d) refers to the constant difference between consecutive terms in a sequence

In mathematics, the common difference (d) refers to the constant difference between consecutive terms in a sequence. It is often used in arithmetic sequences and is denoted by the letter “d”.

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. For example, consider the sequence 2, 5, 8, 11, 14. The common difference in this sequence is 3, as there is a constant increase of 3 between each term.

To find the common difference in an arithmetic sequence, you can subtract any two consecutive terms. For example, in the sequence above, subtracting 5 from 2 gives us 3, subtracting 8 from 5 gives us 3, and so on. Therefore, the common difference is 3.

The common difference is an important characteristic of arithmetic sequences as it allows you to find any term in the sequence given the first term and the position of the term.

For example, in the sequence above, the first term is 2 and the common difference is 3. To find the 10th term, you can use the formula:

nth term = first term + (n – 1) * common difference

Plugging in the values, we get:

10th term = 2 + (10 – 1) * 3
= 2 + 9 * 3
= 2 + 27
= 29

Therefore, the 10th term in the sequence is 29.

In summary, the common difference (d) is the constant difference between consecutive terms in an arithmetic sequence. It allows you to find any term in the sequence and is an important concept in mathematics.

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