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Important Points in Sequence and Series

Important Points in Sequence and Series

1.       Sequence and Series Definition

2.       Different Types of Sequences

(i)                  Finite Sequence

(ii)                Infinite Sequence

(iii)               Increasing Sequence

(iv)              Decreasing Sequence

(v)                Converging Sequence

(vi)              Diverging Sequence

(vii)             Fibonacci Sequence

3.       Progression Types

(i)                  Arithmetic Progression(A.P.)

(ii)                Geometric Progression(G.P.)

(iii)               Harmonic Progression(H.P.)

(iv)              Arithmetico Geometric Progression(A.G.P.)

4.       Arithmetic Progression

(i)                  Definition and Appearance

(ii)                General Term

(iii)               Sum of First n Terms

(iv)              Properties of A.P.

5.       Arithmetic Mean(A.M.)

(i)                  Definition

(ii)                AM of Two Numbers

(iii)               AM of n numbers

(iv)              Weighted AM of n numbers with given weights

(v)                Insertion of n AM between two numbers

(vi)              Sum of all n AM between two numbers

6.       Geometric Progression(G.P.)

(i)                  Definition and Appearance

(ii)                General Term

(iii)               Sum of First n Terms

(iv)              Sum of Infinite terms

(v)                Properties of G.P.

7.       Geometric Mean(G.M.)

(i)                  Definition

(ii)                GM of Two Numbers

(iii)               GM of n numbers

(iv)              Weighted GM of n numbers with given weights

(v)                Insertion of n GM between two numbers

(vi)              Product of all n GM between two numbers

8.       Relation between AM and GM

9.       Arithmetico Geometric Progression(A.G.P.)

(i)                  Definition and Appearance

(ii)                General Term

(iii)               Sum of n terms

(iv)              Sum of infinite terms

10.   Miscellaneous Sequences

(i)                  Sigma Formulae

(ii)                Finding nth term

(iii)               Finding Sum of n terms

(iv)              Type I Method using sigma

(v)                Type II Method using Method of Difference

(a)    Difference of Terms is AP

(b)   Difference of Difference of Terms is AP

(c)    Difference of Terms is GP

(d)   Difference of Difference of Terms is GP

(vi)              Type III Method using Splitting the nth term as difference of two

11.   Harmonic Progression(H.P.)

(i)                  Definition and Appearance

(ii)                General Term

(iii)               No Sum Formula

12.   Harmonic Mean(H.M.)

(i)                  Definition

(ii)                HM of Two numbers

(iii)               HM of n numbers

(iv)              Weighted HM of n numbers with given weights

(v)                Insertion of n HM between two numbers

(vi)              Sum of Reciprocal of n HM between two numbers

13.   Relation between AM, GM, HM

(i)                  Minima Problems

(ii)                Maxima Problems

 

 

 

 


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