NCERT Book Class 11 Maths Chapter 8 Sequences and Series

Chapter 8
SEQUENCES AND SERIES

vNatural numbers are the product of human spirit. – DEDEKIND v

8.1 Introduction
In mathematics, the word, “sequence” is used in much the
same way as it is in ordinary English. When we say that a
collection of objects is listed in a sequence, we usually mean
that the collection is ordered in such a way that it has an
identified first member, second member, third member and
so on. For example, population of human beings or bacteria
at different times form a sequence. The amount of money
deposited in a bank, over a number of years form a sequence.
Depreciated values of certain commodity occur in a
sequence. Sequences have important applications in several Fibonacci
spheres of human activities. (1175-1250)
Sequences, following specific patterns are called progressions. In previous class,
we have studied about arithmetic progression (A.P). In this Chapter, besides discussing
more about A.P.; arithmetic mean, geometric mean, relationship between A.M.
and G.M., special series in forms of sum to n terms of consecutive natural numbers,
sum to n terms of squares of natural numbers and sum to n terms of cubes of
natural numbers will also be studied.
8.2 Sequences
Let us consider the following examples:
Assume that there is a generation gap of 30 years, we are asked to find the
number of ancestors, i.e., parents, grandparents, great grandparents, etc. that a person
might have over 300 years.

Here, the total number of generations = 300 = 10
30