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Definition


A sequence is an arrangement of numbers in a definite order according to some rule. are the terms in a sequence corresponding to 1st, 2nd, 3rd place. In general, the number at the place is called the term (general term) of a sequence and is denoted by .
Eg:- is a sequence whose first term is .
given a sequence, we can find the general term of the sequence.

Example:

Given the term, we can determine the sequence.

Example:
the sequence can be got by substituting
n = 1, 2, 3.....

What is a series?


When the terms of a sequence are connected by plus (+) signs, they are said to form a series.

Example:

, can be shortly written as (read as "Sigma 1 to
n ")

Note:
Σ (Sigma) indicates summation of similar terms.

Example: 1
Find the general term of the sequences 2, 5, 10...

Solution:


Example: 2
Find the general term of the sequences


Solution:


Example: 3
Find the general term of the sequences
1, 3, 7, 15...

Solution:


Example: 4
Find the 3rd and 4th terms of the: sequence if
Solution:


Example: 5
Write the series corresponding to the sequence whose term

Solution:





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