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sequence and series

sequence and series

04/23/2021
Sequence and Series
Edubomb Edubomb

Sequence and series in mathematics

SEQUENCE

The sequence can be defined as the successive arrangement of numbers in definite order with certain given rules. The sequence is said to be finite or infinite according as it has finite or infinite numbers of terms.

For example:

{1, 2, 3, 4,} (it is a finite sequence)

{20, 25, 30, 35, ...} is an infinite sequence

{1, 3, 5, 7} is the sequence of the first 4 odd numbers (and is a finite sequence)

 General term in sequence:

The number occurring at a certain nth place of the sequence is called the nth term or general term which is denoted by tn

Notation:

Sequences use the same notation as the sets. Each element in the list or sequence is separated by a comma and then put a curly bracket around the whole sequence. The element or term of the sequence is usually denoted by a1, a2, a3 …. or t1, t2…. where subscript used are natural numbers and they represent the position of the term in a sequence.

Progression

the sequence of the n items is said to be progression if the sequence follows certain patterns.

For example:

i)                3, 5, 7, 9, …….21

ii)              2, 4, 6, 8……….20

Are sequence. At first, each number are increasing by constant number 2. In second sequence, series is formed adding 2 to the preceding term hence there all are sequence with a certain pattern called the progression.

Series

When sequences are added or subtracted then series is formed. A series may be finite or infinite according to numbers of items in corresponding sequence are finite or infinite. 

For example:

i)                3+5+7+9+12….21

ii)              2+4+6+8+10+…20

Hence these all are series corresponding to above mentions progression.

SOLVED EXAMPLES

Example-1 write the first three terms of the sequence given by t­n=(3n+1)






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