__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*.