Table of Contents
Definition of Sequence and Series
Sequence
A sequence is a set of numbers that are placed in order.
Series
A series is a set of numbers that are placed in order and have a sum.
Types of Sequences
There are many types of sequences, but some of the more common ones are arithmetic, geometric, and harmonic.
An arithmetic sequence is a sequence of numbers in which each number is the sum of the previous two numbers in the sequence. For example, the sequence 1, 2, 3, 4, 5, would be an arithmetic sequence.
A geometric sequence is a sequence of numbers in which each number is the product of the previous two numbers in the sequence. For example, the sequence 1, 2, 4, 8, 16, would be a geometric sequence.
A harmonic sequence is a sequence of numbers in which each number is the reciprocal of the previous number in the sequence. For example, the sequence 1, 1/2, 1/3, 1/4, 1/5, would be a harmonic sequence.
Difference Between Sequence and Series
Sequence:
A sequence is a set of numbers that are placed in a certain order. The numbers in a sequence can be any type of number, including real numbers, integers, or rational numbers. There are a few different types of sequences, but the most common type is a arithmetic sequence.
Series:
A series is a set of numbers that are placed in a certain order and added together. The numbers in a series can be any type of number, including real numbers, integers, or rational numbers. There are a few different types of series, but the most common type is a arithmetic series.
Sequence and Series Formulas
Sequences are a series of numbers that are in a certain order.
The first sequence is 1, 2, 3, 4, 5, 6, 7, 8.
The second sequence is 1, 3, 5, 7, 9, 11, 13.
The third sequence is 2, 4, 6, 8, 10, 12.
The fourth sequence is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.
Sequences can be created by adding or multiplying the previous number in the sequence by a certain number.
The sequence 1, 2, 3, 4, 5, 6, 7, 8 can be created by adding 1 to the previous number.
The sequence 1, 3, 5, 7, 9, 11, 13 can be created by multiplying the previous number by 2.
Formula for Series
The sum of a series can be found by using the following formula:
S = a + (a + d) + (a + 2d) + (a + 3d) …..+(a+xd)
where a is the first term in the series, d is the common difference, and S is the sum of the series.
