NCERT Class 10 Mathematics

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 ak + 1 – ak 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 an = a + (n – 1) d.

4.The sum of the first n terms of an AP is given by :

S = 2(1)✁

2

n an 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 :

S = ()

2

n al

✂

A NOTE TO THE READER

If a, b, c are in AP, then b =

2

ac☎

and b is called the arithmetic

mean of a and c.