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Number Theory Arithmetic progression question


Jan 26, 2012

What is the greatest number a k-term arithmetic progression starting with 1 can end in if each term is less than or equal to n? I'm looking to write this as an expression involving n and k in order to count the number of arithmetic progressions of length k with each term in $[n]$, that is the set of positive integers less than or equal to n.



It was good to ask the question. Here is the answer: 1+(k-1)*floor((n-1)/(k-1)).
If anyone has any remarks, questions as to how the above is true, shoot!

Thanks again,
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