Patterns in Mathematics — Important Questions

1, 3, 6, 10, ...

Triangular numbers start as 1, 3, 6, 10, 15, 21, 28, ... and each term matches a triangle made of dots. The other choices are square numbers, cube numbers, and even numbers, which are different sequences. So only the triangular-number sequence is correct here.

9

Step by step: 1 + 2 = 3, then 3 + 3 = 6, then 6 + 2 = 8, finally 8 + 1 = 9. This follows the 'up and down' pattern that gives square numbers (3²).

1, 2, 3, 4, 5..., Natural numbers, Positive integers

Counting numbers are 1, 2, 3, 4, 5... They are also called natural numbers or positive integers. The sequence 2, 4, 6, 8, 10... represents even numbers, not counting numbers.

15

Add step by step: 1 + 2 = 3, then 3 + 3 = 6, then 6 + 4 = 10, finally 10 + 5 = 15. This is the 5th triangular number.