Pythagroas triples.

My formulas are 1.2n + 1 2.2n2 + 2n 3.2n2 + 2n + 1 4.4n2 + 6n + 2 5.2n3 + 3n2 + n To get these formulas I did the following 1.Take side 'a' for the first five terms 3, 5, 7, 9, 11. From these numbers you can see that the formula is 2n + 1 because these are consecutive odd numbers (2n + 1 is the general formula for consecutive odd numbers) You may be able to see the formula if you draw a graph 2.From looking at my table of results, …

…you equate these equations to 0 you get a2 - 3d2 - 2ad = 0 Change a to x x2 - 3d2 - 2dx = 0 Factorise this equation to get (x + d)(x - 3d) Therefore x = -d x = 3d x = -d is impossible as you cannot have a negative dimension a, a+d, a + 2d Is the same as 3d, 4d, 5d This tells us that the only Pythagorean triples are 3, 4, 5 or multiples of 3, 4, 5 e.g. 6, 8, 10 or 12, 16, 20 etc.