Final answer:
The sequence given - 3, 6, 10 - follows the Triangular Number Pattern where each term is the sum of all natural numbers up to a certain point. The nth term of this sequence can be found using the formula n(n+1)/2.
Step-by-step explanation:
The student's question seems to be about finding a pattern in a sequence of numbers where the sequence goes from 3 squares to 6 to 10. This type of problem typically involves identifying a rule or formula that describes the progression of the sequence. Without more context, it's challenging to determine the exact nature of the 'squares' mentioned, but the sequence follows the pattern of triangular numbers, which are a series of numbers where each number represents the number of dots that can fill an equilateral triangle. In this case:
- 3 is the second triangular number (1+2)
- 6 is the third triangular number (1+2+3)
- 10 is the fourth triangular number (1+2+3+4)
If we continue this pattern, the next number would be the fifth triangular number, which is 15 (1+2+3+4+5). The general formula for the nth triangular number is n(n+1)/2. Therefore, the rule can be defined as Triangular Number Pattern, where the nth term is given by n(n+1)/2.