Notation, Common Difference - Algebra-1

1. Fundamental Concepts

Sequence Notation: In an arithmetic sequence, the symbol is usually used to represent the n-th term in the sequence, where n denotes the position of the term () and represents the first term of the sequence.
Common Difference: In an arithmetic sequence, the difference between two adjacent terms is a constant, which is called the common difference and denoted by the symbol d. It is calculated as (), that is, the latter term minus the former term.

The common difference d is an important indicator to determine whether a sequence is an arithmetic sequence. A sequence is an arithmetic sequence only if the difference between any two adjacent terms in the sequence is equal and constant.
If the first term and the common difference d of a sequence are known, the characteristics of each term in the arithmetic sequence can be determined.

Given that the first term and the second term of a sequence, according to the formula for calculating the common difference , we can get , that is, the common difference of the sequence is .

When calculating the common difference, you only need to subtract the previous term from any subsequent term in the sequence, because this difference is constant in an arithmetic sequence. For example, to calculate the common difference of a sequence, you can select two adjacent terms and and calculate it using .
When the first term and the common difference d are known, they can be used to analyze the variation law of each term in the sequence and determine whether the sequence is increasing () or decreasing ().