What is the rule for this equation.
in: 1 2 3 4 5 6 7 8 9 10
out: 1 3 6 10 15 21 28 36 45 55
The output numbers are called the "triangular" numbers
Have you ever played billiards?
Think of "racking" up the balls in a triangle
in the first row you have 1 ball for a total of 1
in the 2nd row you have 2 balls for a total of 3
in the 3rd row you have 3 balls for a total 6
in the 4th row you have 4 balls for a total of 10
Can you see the pattern, and your input and output numbers?
for the xth row you have n balls for a total of x(x+1)/2
so
f(x) = x(x+1)/2
see
http://mathworld.wolfram.com/TriangularNumber.html