Maths

116 MATHEMATICS
5.5 Summary
In this chapter, you have studied the following points :
1. An arithmetic progression (AP) is a list of numbers in which each term is obtained by
adding a fixed number d to the preceding term, except the first term. The fixed number d
is called the common difference.
The general form of an AP is a, a + d, a + 2d, a + 3d, . . .
2. A given list of numbers a 1
, a 2
, a 3
, . . . is an AP, if the differences a 2
– a 1
, a 3
– a 2
,
a 4
– a 3
, . . ., give the same value, i.e., if a k + 1
– a k
is the same for different values of k.
3. In an AP with first term a and common difference d, the nth term (or the general term) is
given by a n
= a + (n – 1) d.
4. The sum of the first n terms of an AP is given by :
S = ✁
✂ ✄
n
2
2 a ( n 1) d
5. If l is the last term of the finite AP, say the nth term, then the sum of all terms of the AP
is given by :
n
S = ( a ✂ l )
2
A NOTE TO THE READER
If a, b, c are in AP, then b =
mean of a and c.
a c ☎
2
and b is called the arithmetic