MHB Arithmetic progression question

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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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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