Investigating number patterns

Look at this pattern of 10 marbles

Each different coloured row makes a triangle. So you can make a triangle with 3, 6 and 10 marbles.

If you add another row of (5) marbles then there are 15 marbles in the next triangle

To build up the pattern we start with no marbles then add 1, then 2, then 3 then 4 and so on.

So the pattern is made up like this

From this you can see that the next number in the pattern can be worked out by adding 6 to 15 i.e. 6 + 15 = 21