MHB Arithmetic progression question

AI Thread Summary
The discussion centers on finding the maximum value of the last term in a k-term arithmetic progression starting with 1, where all terms must be less than or equal to n. The solution provided is the expression 1 + (k-1) * floor((n-1)/(k-1)). The original poster encourages further questions or remarks regarding the validity of this solution. The thread highlights the importance of formulating the problem clearly to derive an effective mathematical expression. The inquiry and subsequent resolution demonstrate a successful engagement with arithmetic progression concepts.
poissonspot
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Hey,

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.

Thx,

Edit:

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,
 
Last edited:
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Looks like the OP solved his own question, albeit almost 9 years ago.
 
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