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 {tn} is a sequence then we denote the sum of first n
terms of this sequence by Sn and formula is Sn = 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
: tn = 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 Sn = 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.
