# CBSE Class 10th Maths

## Ch-5 Arithmetic Progressions

SEQUENCE:
A sequence is an arrangement of numbers in a definite order and according to some rule.

Example: 1, 3, 5,7,9, … is a sequence where each successive item is 2 greater than the preceding term and 1.

TERMS :
The various numbers occurring in a sequence are called ‘terms’. Since the order of a sequence is fixed, therefore the terms are known by the position they occupy in the sequence.

Example: 1, 3, 5,7,9, …nth is a sequence of term where-

1 = a1 = First term
3 = a2 = second term
5 = a3 = third term
n = an = general term

### Common Difference:

The difference between any two consecutive terms. For any A.P is called Common difference.

Ex : A.P  3, 5, 7, 9.... common difference is 1.

### The general form of an AP:

The general form of an A.P is: (a, a+d,a+2d,a+3d……) where a is the first term and d is a common difference.

In an A.P. with first term a and common difference d, the nth term (or the general term) is given
by.

an = a + (n – 1)d.

Example: To find fifth term put n = 5
a5 = a + (5 – 1)d = a + 4d

## Sum of Terms in an AP:

The sum to n terms of an A.P is
Sn = n/2 [2a + (n – 1)d] or
Sn = n/2 [a + l] where, l is the last term of the finite AP.

### Arithmetic Mean (A.M):

A.M = Sum of terms/Number of terms