SEQUENCE, SERIES AND PROGRESSION

 SEQUENCE.                                                           

An arrangement of numbers in mathematical pattern.

Ex:1.     7 ,12, 27, 22.....

Ex:2.     2 ,4,8,16,32.

Ex:3.     3,5,9,17, ...

Ex:8.     1/5 ,1/7,   1/9, 1/11..….

TYPES OF SEQUENCE:

(1) Finite :  (a) 7,12,17,22

                      (b) 9,18,54,216

(2) Infinite : (a) 7,12,17,22...

                      (b) 3,8,13,18...

SERIES:                                                                   

Addition or subtraction of term of sequence 

Ex:1.     7 + 12 +27 + 22

Ex:2.     2 + 4 + 8 + 16 + 32.

Ex:3.     3 + 5 + 9 + 17, ...

Ex:8.     1/5 + 1/7 +  1/9 + 1/11..….

TYPES OF SERIES:

(1) Finite :  (a) 7 + 12 + 17 + 22

                      (b) 9 + 18 + 54 + 216

(2) Infinite : (a) 7 + 12 + 17 + 22...

                      (b) 3 + 8 + 13 + 18...

PROGRESSION:                                                     

A special type of sequence or series for which it is possible to obtain a formula for the nth terms.

TYPES OF PROGRESSION:

(a). Arithmetic progression (A.P)

(b) GEOMETRY PROGRESSION (G.P)

(c). ARITHMETIC GEOMETRIC PROGRESSION (A.G.P)

(d) HARMONIC PROGRESSION (H.P)

(e). MISCELLANEOUS PROGRESSION 

FIBONACCI SEQUENCE 

a1=a2 = 1.    Tn = Tn-2 + Tn-1

TOPIC OF A.P.

 1.   nth term or general term of an A.P

2. To Find the term from Tn

3. nth term from the end/last

4. First Negative term 

5. Sum of nth term 

6. Tn from Sn

7. Arithmetic mean (A.M)

8. Sum of Arithmetic progression 

9. Choice of terms in an A.P

10. Some Important points.