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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 an –1 , an, …

Here, a1, a2 … etc. are called the terms of the sequence and an is called the general term or nth 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…

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