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What are the deffirent types of sequeces

User Shrek
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1. Arithmetic Sequence: In an arithmetic sequence, each term is obtained by adding a constant value (called the common difference) to the previous term. For example: 2, 5, 8, 11, 14, ...

2. Geometric Sequence: In a geometric sequence, each term is obtained by multiplying the previous term by a constant value (called the common ratio). For example: 3, 6, 12, 24, 48, ...

3. Fibonacci Sequence: The Fibonacci sequence is a special sequence in which each term is the sum of the two preceding terms. It starts with 0 and 1, and subsequent terms are obtained by adding the previous two terms. For example: 0, 1, 1, 2, 3, 5, 8, 13, ...

4. Harmonic Sequence: In a harmonic sequence, each term is the reciprocal of an arithmetic sequence. The terms are obtained by taking the reciprocals of the corresponding terms of an arithmetic sequence. For example: 1, 1/2, 1/3, 1/4, 1/5, ...

5. Quadratic Sequence: In a quadratic sequence, the terms follow a quadratic pattern. The formula for the nth term of a quadratic sequence is given by a quadratic function of n. For example: 1, 4, 9, 16, 25, ...

6. Prime Number Sequence: The prime number sequence consists of the sequence of prime numbers. Prime numbers are numbers greater than 1 that are only divisible by 1 and themselves. For example: 2, 3, 5, 7, 11, 13, 17, ...

These are just a few examples of different types of sequences. There are many other types and variations of sequences in mathematics, each with its own defining characteristics and properties.

User Martin Rohwedder
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