1.Arithmetic Progression:
AP is a sequence of numbers , such that the difference between any two successive numbers in a progression is a constant.
e.g 2,4,6,8... here the common difference ( d ) is 2 .
An AP will be of the form a , ( a+d ) , ( a + 2d ) , ( a + 3d ) , ( a + 4d ), .. .. ..
Property:
1. a1 + an = a2 + an-1 = ... = ak + an-k+1
2. Formulae for nth term can be defined as an = 1/2(an-1 + an+1)
3. If initial term of AP and the difference is given, then the progression is given by .an = a1 + (n - 1)d, n = 1, 2, ...
4. The sum S of the first n values of a finite swquence is given by S = 1/2(a1 + an)n , where a1 is the first term and an is the last term.
5. If the difference and the first term is given, then the sum S can be calculated by
S = 1/2(2a1 + d(n-1))n .
Geometric Progression:
Any progression or sequence with successive terms having a common ration is called geometric progression.
e.g : 2,4,8,16...
In the ratio is 2 for any two successive terms.
A GP is of the form : a , ar , ar^2 , ar^3 ... where a is the first term and r is common ratio .
The nth term can be find by tn = ar ^ (n-1).
Sum of n terms is . Sn = a( 1 - rn )/ ( 1 - r ).
In case r lies between -1 and + 1 then Sum of all terms : a / ( 1 - r )
Categories:
Aptitude
