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.
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
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
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 termsNCERT Solutions Ch- 5 Maths