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Arithmetic progression(A.P.), Geometric progression (G.P), Harmonic progression (H.P) , nth term , sum of n terms, of A.P. and G.P sum of infinite number of terms of a G.P , sum of the first n natural numbers, sum of the squares of the first n natural numbers and sum of the cubes of the first n natural numbers
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Progressions
Arithmetic Progressions (A. P.)
The sequence a , (a +d ), (a +2d ), (a +3d ), (a +4d ), . . . is called an arithmetic progression.
' a ' is the first term and ' d ' is the common difference of the A.P.
The nth term of the A.P. is a + ( n-1)d
The
sum of n terms of the A.P. is
=
[ 2a + (n - 1 ) d ]
or
=
[
+
]
where
and
are the first and nth terms of the A.P.
Three numbers a , b, c are in A.P. if 2b = a +c.
Geometric Progression (G.P. )
The
sequence a , a r,
,
. . . is called a geometric progression.
' a' is the first term and ' r ' is the common ratio of the geometric progression.
The
nth term of the G.P. is
=
The
sum of n terms of the G.P. is
=
or
=
.
Three
numbers a , b, c are in G.P. if
.
The
sum of infinite number of
terms of the G.P is
=
,
provided
.
Harmonic Progression (H.P.)
The
sequence
,
. . . are said to be in Harmonic Progression if their reciprocals
,.
. . are in Arithmetic Progression.
Sum of the first n natural numbers, 1+2+3+
... + n =
Sum of squares of the first n natural numbers, 12+22+32+
... + n2 =
Sum of the cubes of the first n natural numbers, 13+23+33+
... + n3 =
