Page 10 - Ganit Kaushal

Power of a Natural Number

When we multiply a natural number 2 (say) by itself ‘n’ times, that is, 2 × 2 × 2 × … n-times, then this is
n
written as ‘2 ’ and is read as ‘2 raised to the power n’ or simply ‘2 to the power n’, where ‘n’ itself is a natural
number. Here, we give a few examples for understanding:

4
2 = 2 × 2 × 2 × 2 = 16; Remark
5
3 = 3 × 3 × 3 × 3 × 3 = 243;
Any number raised to the power 0 is taken as
3
4 = 4 × 4 × 4 = 64, … etc. 1, i.e., a = 1 for any number a.
0
Successor and Predecessor
The number that comes just after a given number is called the successor of that number. The number which
comes just before a given number is called the
predecessor of that number. Remember

To find the successor of a given natural number, we 1. Every natural number has a successor.
add 1 to the given number and to find the predecessor 2. The natural number 1 has no predecessor.
of a given natural number, we subtract 1 from the given
number.

Ex 1. What is the successor of 12, 25, 69, 99, 108, 326, 874 and 9999?
Sol. Successor of
12 is 12 + 1 = 13; 25 is 25 + 1 = 26; 69 is 69 + 1 = 70;
99 is 99 + 1 = 100; 108 is 108 + 1 = 109; 326 is 326 + 1 = 327;

874 is 874 + 1 = 875; 9999 is 9999 + 1 = 10,000.
Ex 2. What is the predecessor of 11, 151, 183, and 1000?
Sol. Predecessor of
11 is 11 – 1 = 10; 151 is 151 – 1 = 150; 183 is 183 – 1 = 182;
1000 is 1000 – 1 = 999.

1.2 PATTERNS IN MATHEMATICS AND NATURE

A pattern in mathematics is a sequence or arrangement of numbers, shapes, or objects that follows a specific
rule or a set of rules. Patterns help us recognise order and predict what comes next. They are important because
they form the foundation for many mathematical concepts and problem-solving techniques. In mathematics,
patterns are fun and a powerful way to learn and analyse things.
Among the most basic patterns that occur in mathematics are patterns of whole numbers:

{0, 1, 2, 3, 4, ....}
1. Numbers: Number patterns, like counting by twos (2, 4, 6, 8, ...), are common. Arithmetic patterns
(adding or subtracting the same amount) and geometric patterns (multiplying by a fixed number) help us
understand sequences.
Examples: (a) Even Counting Numbers: 2, 4, 6, 8, 10, ...

(b) Odd Counting Numbers: 1, 3, 5, 7, 9, ...
(c) Multiples of 3: 3, 6, 9, 12, 15, ...

8 Mathematics-6