PROGRESSION

A succession of numbers formed and arranged in a definite order according
to certain definite rule is called a progression.

1.Arithmetic Progression:-If each term of a progression differs from its
preceding term by a constant.
This constant difference is called the common difference of the A.P.
The n th term of this A.P is Tn=a(n-1)+d.
The sum of n terms of A.P Sn=n/2[2a+(n-1)d].

xImportant Results:

a.1+2+3+4+5......................=n(n+1)/2.
b.12+22+32+42+52......................=n(n+1)(2n+1)/6.
c.13+23+33+43+53......................=n2(n+1)2/4

2.Geometric Progression:-A progression of numbers in which every 
term bears a constant ratio with ts preceding term.
i.e a,a r,a r2,a r3...............
In G.P Tn=a r n-1
Sum of n terms Sn=a(1-r n)/1-r