How to do Sequences?

Sequence is defined as any Set of objects or data in a particular format. It forms a series of definite format or of defined interval. Sequences may be of three types termed as arithmetic sequence, geometric sequence, and harmonic sequence. Sequence of Numbers which posses a constant difference between two consecutive terms is known as Arithmetic sequence. Thus we can say that for any sequence to be arithmetic it needs to have a constant difference. Now for knowing about how to do sequences we have to add a constant term to the series of numbers, when a constant term is added next term of sequence is obtained.
                                                                                       
This constant term is defined as common difference and it is denoted by ‘d’. Its first term is denoted by ‘a’, last term is denoted by an and determined by formula “a + (n - 1) d”. Sum of series is denoted by S_n and it is determined by the formula “n/2[2a + (n-1) d]”. To learn how to do sequences in Geometric Progression firstly we must know what geometric progression is. Geometric series is defined as the series in which Ratio of two consecutive terms is constant. Thus, it is defined as a series in which a constant term is multiplied to the terms of series to obtain the next term, this constant term which is multiplied to the terms is known as common ratio which is denoted by ‘r’, its first term is denoted by ‘a’, sum of series is denoted by S_n which is equals to Sn = a (1 – rⁿ⁺¹) / (1 - r) and its last term an is determined as ar^n-1.
 
 Third type of series is defined as Harmonic series which is inverse of Arithmetic Series, it is same as Arithmetic Progression but the difference is that it is reciprocal of that arithmetic progression.