Sequence and Series of Real Numbers

• Sequence: A sequence is an arrangement of numbers in definite order according to some rule.

Also, we define a sequence as a function whose domain is the set of natural numbers or some subset of the type {1, 2, 3… k}.

• • A sequence containing finite number of terms is called a finite sequence.
  • sequence containing infinite number of terms is called an infinite sequence.

 

• A general sequence can be written as

a₁, a₂, a₃ … a_{n –1 ,} a_n, …

Here, a₁, a₂ … etc. are called the terms of the sequence and a_n is called the general term or n^th of the sequence.

• Fibonacci sequence: An arrangement of numbers such as 1, 2, 4, 6, 10 … has no visible pattern. However, the sequence is generated by the recurrence relation given by

This sequence is call…