Plus One Maths Notes Chapter 9 Sequences and Series is part of Plus One Maths Notes. Here we have given Kerala Plus One Maths Notes Chapter 9 Sequences and Series.

Board | SCERT, Kerala |

Text Book | NCERT Based |

Class | Plus One |

Subject | Maths Notes |

Chapter | Chapter 9 |

Chapter Name | Sequences and Series |

Category | Plus One Kerala |

## Kerala Plus One Maths Notes Chapter 9 Sequences and Series

- A sequence is an arrangement of numbers or terms in a definite order according to some rule.
**Finite sequence:**A sequence containing a finite number of terms.**Infinite sequence:**If the sequence is not a finite sequence.- Given a sequence a
_{1}a_{2}, …, a_{n}. Then the expression a_{1}+ a_{2},+……….. + a_{n}is called a series associated with the given sequence, denoted by

**Arithmetic progression (A.P):**A sequence is said to be an A.P, if the difference between every two consecutive terms is always same. This constant is called common difference (d).**Notations:**a – First term, l- last term, d – common difference, n – number of terms, S_{n}– sum to n terms.

l= a + (n – 1) d

- If a, A, b are in A.P, then A is called arithmetic mean between the numbers ‘a’ and ‘b

i.e, - If a non-zero constant is added or subtracted or multiplied or divided to each term of an A.P, then the resulting sequence

is also an A.P. **Geometric Progression (GP.):**A sequence of non-zero numbers is said to be G.P, if the ratio of each term, except the first one, by its proceeding term is always the same. This ratio is called common ratio and is denoted by ‘r’

- If a, G b are in G.P, then G is called geometric mean between the numbers ‘a’ and ‘b’ i.e,
- Arithmetic mean is greater than or equal to Geometric mean. A ≥ G
- Sum of first ‘n’ natural numbers is

- Sum of the squares of first ‘n’ natural numbers is

- Sum of the cubes of first ‘n’ natural numbers is

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