Sequence and Series
Sequence
A sequence is a
function whose domain is the set N of natural numbers.
a1,
a2,
a3,
. . ., an,
. . .
Series
If a1,
a2,
a3,
. . ., an,
. . .is a sequence,
the expression a1+a2+a3+
. . . +an+
. . .
is called a series.
Arithmetic Progression
A sequence is called
an arithmetic progression (A.P.) if the difference between any term and the
previous term is constant.
The constant
difference, generally denoted by d is called the common difference.
a1 =
a, a2 =
a+d, a3 =
a+d+d = a+2d ,
a4 =
a+d+d+d = a+3d
Choose Right term!!
Geometric Progression
A sequence is called
a geometric
progression (G.P.) if the ratio between any
term and the previous
term is constant.
The constant ratio,
generally denoted by r is
called the common ratio.
a1 =
a, a2 =
ar, a3 =
ar2, a4 =
ar3
Choose Right term!!
Harmonic Progression
Arithmetic Mean
A is the A.M. of two
numbers a and b
Û a, A, and b are in A.P.
\ A-a
= b-A
\ 2A = a+b
Inserting n A.M between 2 numbers
Geometric Mean
G is the G.M. of a
and b
Û G2 = ab
Inserting n G.M between 2 numbers
Harmonic Mean
Inserting n H.M between 2 numbers
Relation Between A.M., G.M. And H.M.
Let A, G and H be the
arithmetic, geometric and harmonic means of two positive numbers a and b.
G2=AH
Arithmetico-Geometric
Progression
A sequence is called
an arithmetico-geometric
progression (A.G.P.) if the nth term is a product of
the nth
term of an A.P. and the nth term of a G.P.
Sigma notation
Logarithmic Series
Exponential Series
