## sequence and series

## 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 t_{n}

**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
a_{1,} a_{2,} a_{3} …. or t_{1}, t_{2}…. 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 t_{n}=(3n+1)

- VIA
- Edubomb

- SOURCS
- Author G.B. Budhathoki

## LEAVE A COMMENT

## Facebook Conversations