What is the next number in the sequence of triangular numbers: 1, 3, 6, 10, …?
Triangular numbers are numbers that can be arranged in the shape of an equilateral triangle. Each term in the sequence represents the total number of dots that can form a triangle. Examples include 1, 3, 6, 10, 15, and so on. They follow the formula n(n+1)/2.
Patterns in mathematics involve identifying regularities in numbers shapes and arrangements. These patterns can be numerical geometric or logical. Recognizing patterns improves problem-solving skills and logical thinking. It helps students predict future terms in sequences and understand complex concepts which is vital for mastering advanced mathematical topics.
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Triangular numbers are in the form that every number denotes the sum of dots that make up an equilateral triangle. The formula for the nth triangular number is given as:
Tₙ = n(n + 1) /₂.
For the following sequence:
T₁ = 1, T₂ = 3, T₃ = 6, T₄ = 10.
The following number in the sequence is T₅ = 5(5 + 1) /₂ = 15.
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