Chap -5
ARITHMETIC PROGESSION
SOME
IMPORTANT FACTS
1. A sequence
is an arrangement of numbers in a definite order according to some rule.
2. An Arithmetic Progression is a sequence in
which terms increases or decreases regularly by adding the same constant/ fixed number d to the
preceding term. This constant “d” is
called the common difference of the
progression (series) can be positive, negative or zero.
3. We usually denote first term of A.P by “a” the common difference “d” and last term “l”. Arithmetic
Progression represented by
a, a+d, a+2d, a+3d,………….., this is
the General form of AP.
Common Difference “d” = a2-a1=a3-a2=a4-a3=………..=
an- an-1, where an
is nth term of AP.
4. In general
, if a n+1 – an
is same for different values of n or in other words, a n+1
– an is independent of n.
5. The nth
term / last term of an AP with first term a and common difference d is ;
An=l=
a+ (n-1)d.
6. The sum of
first terms of AP is given by ;
i)
S n
= n(a + l)/2
ii) S n = n[2a + (n-1)d ]/2 ;
a is first term , l is last term