An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference, denoted by the letter "d".

The general form of an arithmetic sequence is:

a₁, a₁ + d, a₁ + 2d, a₁ + 3d, ...

Where:

a₁ is the first term of the sequence
d is the common difference

Formula for the n^th Term

The formula to find the n^th term of an arithmetic sequence is:

a_n = a₁ + (n - 1)d

Formula for the Sum of the First n Terms

The formula to find the sum of the first n terms of an arithmetic sequence is:

S_n = (n/2)(a₁ + a_n)

Study Guide

When working with arithmetic sequences, it's important to understand the concept of a common difference and how it affects the sequence. Here are some key points to remember when dealing with arithmetic sequences:

Identify the first term (a₁) and the common difference (d) from the given sequence.
Use the formula a_n = a₁ + (n - 1)d to find the value of any term in the sequence.
To find the sum of the first n terms, use the formula S_n = (n/2)(a₁ + a_n).
Practice finding the n^th term and the sum of the first n terms for different arithmetic sequences.

Understanding arithmetic sequences is important as they are widely used in various mathematical and real-world applications. Regular practice and application of the formulas will help in mastering this concept.