In how many ways can you select 3 distinct numbers from a set of x distinct natural numbers (the set is starting from 1 and ending at x) such that the 3 numbers that you selected are in arithmetic progression?
2026-03-27 10:31:40.1774607500
How many ways of selection?
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If three numbers a,b,c are in an Arithmetic Progression, then it follows that $b=\dfrac{a+c}{2}$. Since $b$ is an integer, $a+c$ must be even: Which further means that there are 2 cases for $a$ and $c$: Which I leave for you to find. As Christian Blatter pointed out, $a$ and $c$ completely determine the triple.