__Definitions and Formulas__

A collection of numbers
arranged in a definite order according to some definite rule is called a sequence. e.g. 1,5,9,13,.....

If {t

_{n}} is a sequence then we denote the sum of first*n*terms of this sequence by S_{n}and formula is S_{n}= n(n+1)/2.
A special type of
sequence in which the relationship between any two consecutive terms is the
same is called a progression. e.g. 1,4,9,16,....

A sequence such that for
a given first term, each term can be obtained by adding a fixed number to the
preceding term is called an Arithmetic
Progression. The fixed number is
called common difference and is denoted by

*d*. e.g. A.P. =*a,a+d,a+2d,a+3d,*....
Formula for general term
: t

_{n}= a+(n-1)d.
Formula for sum of first

*n*terms of an A.P. whose first term is*a*and the common difference is*d*is S_{n}= n/2 [ 2a+ (n-1)d]._{ }

For an A.P. whose first
term is

*a*and common difference is*d*, if any real number*k*is added to each term of the A.P. then the new sequence is also an A.P. with first term*a+k*and common difference*d*.