NCERT Book Class 9 Mathematics Chapter 8 Predicting What Comes Next: Exploring Sequences and Progressions

Predicting What Comes Next:
Exploring Sequences and
8 Progressions

8.1 Introduction to Sequences
We see patterns around us everywhere, be it in nature, in art, in music,
in finance and in many other contexts in everyday life. Patterns help us
make sense of the world and predict what comes next. In mathematics,
sequences are special kinds of patterns formed by numbers or other
objects arranged in a particular order. By understanding sequences,
we can explore fascinating ideas about how numbers grow, shrink, or
repeat and even use these ideas to solve real-life problems.
In this chapter, we shall explore patterns in sequences of numbers.
We will then find rules to help us predict more numbers of the sequence.
Let us begin by looking at some number sequences that you have already
seen in Grades 6, 7 and 8.

1, 2, 3, 4, 5, 6, … (Natural Numbers)
1, 3, 5, 7, 9, 11, ... (Odd Numbers)
1, 3, 6, 10, 15, 21, ... (Triangular Numbers)
1, 4, 9, 16, 25, 36, ... (Square Numbers)

The three dots … indicate that the sequence continues indefinitely.

Think and Reflect
Can you describe the pattern in each of the above sequences? Can you
predict the next few numbers in these sequences?

Before we proceed, let us define a sequence as an ordered list of
numbers where each number is a term of the sequence. Thus, in the
sequence of square numbers, 1 is the first term, 4 is the second term,
25 is the fifth term and so on. Also, sequences may be finite or infinite.
The sequences mentioned above are infinite. But the sequence 6, 12, 24,
48, 96 is a finite sequence of five terms. Can you think of other finite
sequences that you see in your daily life?