sequences

progressions

I)Arithmetic progression (AP) : sequence of numbers such that the difference of any two successive members of the sequence is a constant.

a, a+d, a+2d, a+3d, ....., (a+(n-1)*d)

example:
               3,5,7,9,11,.........,(3+(n-1)*2)
Here,
        2 is common difference (d).
        3 is first number (a).
        n'th number of this sequence is (a+(n-1)*d)


II)Geometric progression (GP) : sequence of numbers such that the quotient of any two successive members of the sequence is a constant.

 a, a*r, a*r², a*r³,.....,a*r^n-1

example:
               4,12,36,108,324,........,4*3^n-1
Here,
        3 is common ratio (r).
        4 is first number (a).
        n'th number of this sequence is (a*r^n-1)

III) Harmonic Progression (HP) : is a progression formed by taking the reciprocals of an arithmetic progression. 

1/a, 1/(a+d), 1/(a+2d),......, 1/(a+(n-1)*d)

example:
               1/3,1/7,1/11,1/15.........[1/(3+(n-1)*4]     in hp   because  3,7,11,15 are in ap.


Find next two numbers..

level 1:

1) 4 , 8 , 12 , 16 , ... , ....
2) 1 , 6 , 36 , ... , ....
3)  1/8 , 1/10 , 1/12 , ... , ....
4) 3 , 15 , 75 , ... , ....
5) 12 , 10 , 8 , 6 , ... , ....

level 2:

1)  2, 1, 0.666, 0.5 , ... , ....
2)  3, -3, 3 , ... , ....
3)  1/2, 3/4, 1 , ... , ....
4)  3, 4, 5.333 , ... , ....
5)  0.6, -1.2, 2.4 , ... , ....

level 3:
1)  1, 2,  , ... , ....
        a)3,4     b)4,8   c) infinity,-2  d) a & b  e) a,b&c


Answers