Table of Contents
Sequences and Series Meaning
Sequences and series are mathematical objects that allow us to model the real world. A sequence is a set of numbers that are in order. A series is a sum of the numbers in a sequence.
One of the most important sequences is the Fibonacci sequence. It is named after Leonardo Fibonacci, who discovered it in the 13th century. The Fibonacci sequence is defined as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765.
The next number in the sequence is the sum of the previous two numbers.
| S.NO | CONTENT |
| 1 | INTRODUCTION |
| 2 | ABOUT SEQUENCES AND SERIES |
| 3 | SEQUENCES AND SERIES |
| 4 | TYPES OF SEQUENCES AND SERIES |
About Sequence and Series
Sequence:
A sequence is an ordered list of numbers. The first number in the sequence is called the “initial value” and the second number is called the “increment.” The increment is always one more than the previous number in the sequence.
For example, the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is generated by starting with 1 and incrementing by 1 each time.
The third number in the sequence is 2 because 1 + 1 = 2. The fourth number is 3 because 1 + 2 = 3, and so on.
Series:
A series is a sum of the numbers in a sequence.
For example, the series 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is the sum of the numbers in the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Sequence and Series
Sequences are sets of numbers that are listed in a specific order. A sequence can be created by listing the first few terms of a sequence, or by describing a pattern that the terms follow.
Series are collections of sequences that are related to each other. A series can be created by combining the terms of several sequences, or by creating a sequence that is based on the terms of another sequence.
Types of Sequence and Series
Some of the most common examples of sequences are:
- Arithmetic Sequences
- Geometric Sequences
- Harmonic Sequences
- Fibonacci Numbers
Arithmetic Sequences
A sequence in which every term is created by adding or subtracting a definite number to the preceding number is an arithmetic sequence.
Geometric Sequences
A sequence in which every term is obtained by multiplying or dividing a definite number with the preceding number is known as a geometric sequence.
Harmonic Sequences
A series of numbers is said to be in harmonic sequence if the reciprocals of all the elements of the sequence form an arithmetic sequence.
Fibonacci Numbers
Fibonacci numbers form an interesting sequence of numbers in which each element is obtained by adding two preceding elements and the sequence starts with 0 and 1. Sequence is defined as, F0 = 0 and F1 = 1 and Fn = Fn-1 + Fn-2
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