By doubling a triangle number we can create a rectangle
I noticed the dimensions were of the form n and n+1 (3 and 4, 4 and 5 and so on)
The dimenesions of the 250th triangle number are 250 and 251
These dimensions give us a rectangle of size 250 x 251 which equals 62750
However, this rectangle size is twice the 250th triangle number so we divide by 2 to get the triangle number
62750 / 2 = 31375
Therefore 31375 is the 250th triangle number
The strategy I use to find any triangle number can be shown by the following
equation I worked out
t = n(n + 1)
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2
The triangle numbers are: 4851, 3655, 7626
The method I used to determine if a number is a triangle number is as follows:
First I double the number to give the rectangle's size
I then get the square root of the number and round it down to give the smaller size of the rectangle - call this n
I then multiply n by n + 1, if this is the same size as the rectangle then this is a triangle number
Yes, it is possible to have a triangle number ending in 000
If we, say, consider the 2000th triangle number
this would be 2000 x 2001 / 2 which equals 2001000