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

Can you describe the pattern in each of the above sequences? Can you predict the next few numbers in these sequences?                                                                                                                                                                                                 [Page No. 174]

Each of the four sequences follows a clear rule, so the next terms can be predicted with confidence.

Natural numbers 1, 2, 3, 4, 5, 6, ... : every term is 1 more than the term before it.

Next few terms: 7, 8, 9.

Odd numbers 1, 3, 5, 7, 9, 11, ... : the difference between any two consecutive terms is 2.

Next few terms: 13, 15, 17.

Triangular numbers 1, 3, 6, 10, 15, 21, ... : the differences themselves grow by 1 each time (2, 3, 4, 5, 6, ...), and each term is the sum of the natural numbers up to that position.

Adding 7, then 8, then 9 gives the next terms: 28, 36, 45.

Square numbers 1, 4, 9, 16, 25, 36, ... : each term is $n^2$, and the differences are the odd numbers 3, 5, 7, 9, 11.

Next few terms: 49, 64, 81.