Question

How can 1 be a triangular number. I know that 3 can be a triangular but how can 1 be triangular number

Answer 1

We commonly do this in mathematics: we define a term initially based on an observation (such as that certain numbers of dots can form a triangle), then extend the definition a little more broadly (in this case, as a number that can be written as a sum of consecutive numbers starting at 1), and find that the new definition includes a case that is "on the edge" of this definition, namely when there is only one row of dots, so we are only adding one "consecutive number", 1 itself. It doesn't really look like a triangle (though you can stretch your mind and see it that way!), but it does continue the pattern of triangular numbers and gives a good starting point for the sequence A triangular number is the number of dots needed to draw a triangle. This is one kind ofpolygonal number. Here is a picture of the first few triangular numbers: * * * * * 1 * * * * * * * * 3 * * * * * * * * * 6 * * * * * * * * 10 * * * * * 15

The formula for the nth triangular number is T(n) = n (n+1)/2.