Series And Sequences

A sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule. If a1, a2, a3, a4,……… etc. denote the terms of a sequence, then 1,2,3,4,…..denotes the position of the term.

A sequence can be defined based on the number of terms i.e. either finite sequence or infinite sequence.

If a1, a2, a3, a4, ……. is a sequence, then the corresponding series is given by

SN = a1+a2+a3 + .. + aN

Note: The series is finite or infinite depending if the sequence is finite or infinite.

Types of Sequence and Series

Some of the most common examples of sequences are:

Arithmetic Sequences

Geometric Sequences

Harmonic Sequences

I will be writing on the first two

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.