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## CBSE Guide Sequences And Series class 11 Notes

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## Sequences And Series class 11 Notes Mathematics

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**CBSE Class 11 Mathematics Revision Notes Chapter-9 Sequences And Series class 11 Notes Mathematics **

**1. Sequences and series 2. Arithmetic Progression (A.P.) 3. Geometric Progression (G.P.), relation in A.M. and G.M. 4. Sum to n terms of Special Series**

**Sequence**: By a sequence, we mean an arrangement of number in definite order according to some rules. Also, we define a sequence as a function whose domain is the set of natural numbers or some subsets of the type {1, 2, 3, ….k}. A sequence containing a finite number of terms is called a finite sequence. A sequence is called infinite if it is not a finite sequence.- Let , … be the sequence, then the sum expressed as is called series. A series is called finite series if it has got finite number of terms.

**ARITHMETIC PROGRESSION**

- An arithmetic progression (A.P .) is a sequence in which terms increase or decrease regularly by the same constant. This constant is called common difference of the A.P. Usually, we denote the first term of A.P . by a, the common difference by d and the last term by
^{th}term of the A.P. is given by . The general term or the n - Single Arithmetic mean between any two given numbers a and b: A.M. =
- Arithmetic mean between two given numbers a and b: form an A.P.
- If a constant is added to each term of an A.P., then the resulting sequence is also an A.P.
- If a constant is subtracted to each term of an A.P., then the resulting sequence is also an A.P.
- If each term of an A.P. is multiplied by a constant, then the resuting sequence is also an A.P.
- If each term of an A.P. is divided by a constant, then the resuting sequence is also an A.P.
- Sum of first terms of an A.P.: and , where is the last term, i.e., .

**GEOMETRIC PROGRESSION**

- A sequence of non-zero numbers is said to be a geometric progression, if the ratio of each term, except the first one, by its preceding term is always the same. , where is the first term and is the common ratio.
- term of a G.P.:
- Sum of terms of a G.P.: if .
- Sum to infinity of a G.P.:
- Geometric mean between a and b:
- Geometric means between a and b:
- If all the terms of a G.P. be multiplied or divided by the same quantity the resulting sequence is also a G.P.
- The reciprocal of the terms of a given G.P. form a G.P.
- If each term of a G.P. be raised to the same power, the resulting sequence is also a G.P.

**ARITHMETIC – GEOMETRIC SERIES**

- A sequence of non-zero numbers is said to be a arithmetic-geometric series, if its terms are obtained on multiplying the terms of an A.P. by the corresponding terms of a G.P. For example:
- The general form of an arithmetic-geometric series:

- n
^{th}term of an arithmetic-geometric series: of A.P. x of G.P. - Sum of n terms of some special series :
- Sum of squares of first n natural numbers =
- Sum of cubes of fist n natural numebrs =

## The Sequences And Series class 11 Notes

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