Introduction to Sequences
Learn about Sequences
What are Sequances in your opinion? A number that starts with 2 and jumps by 2 every time, like 2, 4, 6, 8, 10, and so on is called a sequence.
Sequences are sets of numbers arranged in a specific order or pattern. They are often used to study patterns in mathematical equations and in real-world phenomena. There are two types of sequences: arithmetic and geometric.
Arithmetic sequences are sequences where each number is a fixed distance or interval from the previous number. This interval is called the common difference. For example, the sequence 1, 3, 5, 7, 9 is an arithmetic sequence with a common difference of 2, since each number is 2 more than the previous number.
Geometric sequences, on the other hand, are sequences where each number is a fixed multiple of the previous number. This fixed multiple is called the common ratio. For example, the sequence 1, 2, 4, 8, 16 is a geometric sequence with a common ratio of 2, since each number is twice the previous number.
Sequences can be used to model a wide variety of phenomena, such as population growth, financial investments, and even the structure of DNA. They are also an important concept in calculus, where they are used to study the behavior of functions and limits.