TN samacheer kalvi 10th Maths:
Chapter 2 Numbers and Sequences – Exercise 2.5 Introduction
Arithmetic
Progression(A.P):
Arithmetic
Progression is a sequence whose successive terms differ by a constant number called common difference.
1.
The general form of the A.P is
|
a, |
a +
d, |
a +
2d, |
a + 3d, |
…. |
a+(n-1)d |
|
(t1) |
(t2) |
(t3) |
( t4) |
…. |
(tn) |
2.
Common difference (d) = t2 –
t1
3.
nth term: tn =
a + (n-1)d
4.
Number of terms:
n = [(l-a)÷d] + 1
a - First term
d - Common difference
tn - Nth term
n - number of terms
l - last term
t2 - second term
t1 - first term
5.
Important properties/Notes:
i.
If there are finite numbers of terms in an A.P. then it is
called Finite Arithmetic Progression. If there are infinitely many terms in an A.P.
then it is called Infinite Arithmetic Progression.
ii.
The common difference of an A.P. can be positive, negative or
zero.
iii.
An Arithmetic progression having a common difference of zero
is called a constant arithmetic progression.
iv.
The common difference of a constant A.P. is zero.
v.
If a and l are first and last terms of an A.P. then the
number of terms is one.
vi.
If the sum of three consecutive terms of an A.P. is given,
then they can be taken as a -d, a and a +d. Here the common difference is d.
vii.
If the sum of four consecutive terms of an A.P. is given
then, they can be taken as a -3d , a -d , a +d and a + 3d . Here common
difference is 2d.
viii. Three non-zero numbers
a, b, c are in A.P. if and only if 2b = a +c