Classical algebra arivu ap,gp,hp

16SCCMM6

1. CLASSICAL ALGEBRA D.ARIVUSELVI

2. SYNOPSIS Arithmetic progression Geometric progression Harmonic progression

3. ARITHMETIC PROGRESSION A sequence of the form, a,a+d,a+2d,a+3d,......a+(n-1)d,a+nd,.... is called an arithmetic progression (or) sequence. Here, a=First term d=Common difference The n th term of an arithmetic progression is given by,

4. EXAMPLES Common difference= 12 , 9 , 6 , 3 ,........................................ Common difference = -3

5. GEOMETRIC PROGRESSION A sequence of the form, with a ≠ 0, r ≠ 0 is called a geometic progression (or) sequence . Here r = Common ratio , a=First term The n th term of a geometric progression is given by,

6. EXAMPLES 1 , 2 , 4 , 8 , 16,....... Common ratio=2 Common ratio =

7. HARMONIC PROGRESSION A sequence h1 , h2 , h3,........is said to be a harmonic sequence (or )harmonic progression if is an arithmetic sequence The general harmonic mean will be of the form

8. EXAMPLES is a harmonic sequence. It is the reciprocal of Arithmetic progression.

9. SYMMENTRIC FUNCTION If a function involving all the roots of an equation is unaltered in value any two of the roots are interchanged it is called a symmetric function of the roots

10. FORMULAE When the higher degree is 3,

11. When the higher degree is 4,

12. END