Sequences and series

In mathematics, one of the important topics that come under the basic study of mathematics is sequences and series. Sequences originally suggest an ordered list of objects. Again sequence suggests the sum of sequences. In mathematics both these terms comes together and come under the study of calculus as sequences and series. The series that is uncountable is called infinite series and if any series end in finite terms it is called finite series. While sequence like {1,2,3,4,5,6,7} is a finite series, sequence like {1,2,3,4,…….} is an example of infinite series. These are simple sequences in mathematics. Sequences and series are mainly classified into two branch study: Arithmetic sequence and geometric sequence.

Arithmetic sequence is also stated as arithmetic progression or arithmetic mean. When in a sequence the difference between each object is constant, that sequence is called arithmetic progression. Arithmetic progression is represented with the sequence: {a, a+2d, a+3d, a+4d…}

Geometric progression or geometric sequence or geometric mean is another type of mathematical sequence. It is a sequence where each term is found by multiplying the previous term by a constant. Geometric progression is represented with the sequence: {a, ar, ar², ar³…}

Besides these two series there is another type of series which is called as harmonic series. Harmonic series is a divergent series that is infinite. Harmonic series or mean is represented with the sequence: {1 + a+½ + a+¼…}

These are the three main types of series in mathematics. Arithmetic mean, geometric mean and harmonic mean are the most important concepts of mathematics. This study of sequences and series comes under the middle grade math studies. To learn it better it is very important to understand the series and the differences between each series thoroughly. Students can take more help on this concept from online and benefited. Learn the sequences and series and improve math knowledge.