Common Difference d
In mathematics, the common difference (d) refers to the difference between any two consecutive terms in an arithmetic sequence
In mathematics, the common difference (d) refers to the difference between any two consecutive terms in an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a constant value (the common difference) to the previous term.
To find the common difference of an arithmetic sequence, you can compare any two consecutive terms. If you subtract the first term from the second term, or the second term from the third term, or any other consecutive terms, you should obtain the same value, which is the common difference.
For example, let’s consider the arithmetic sequence: 2, 5, 8, 11, 14, 17, …
To find the common difference, we can subtract the first term (2) from the second term (5):
5 – 2 = 3
Similarly, if we subtract the second term (5) from the third term (8):
8 – 5 = 3
And if we subtract the third term (8) from the fourth term (11):
11 – 8 = 3
As you can see, in this particular arithmetic sequence, the common difference is 3. This means that each term is obtained by adding 3 to the previous term.
The concept of common difference is crucial in arithmetic sequences, as it allows us to determine subsequent terms without having to write out the entire sequence. By knowing the first term and the common difference, we can use the formula for the nth term of an arithmetic sequence (an = a1 + (n-1)d) to find any specific term in the sequence.
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