Arithmetic progression question

In summary, the greatest number that a k-term arithmetic progression starting with 1 can end in is 1 + (k-1) * floor((n-1)/(k-1)), where each term is less than or equal to n. This expression can be used to count the number of arithmetic progressions of length k with each term in the set of positive integers less than or equal to n. The answer was provided by the OP almost 9 years ago.
  • #1
poissonspot
40
0
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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  • #2
Looks like the OP solved his own question, albeit almost 9 years ago.
 

FAQ: Arithmetic progression question

1. What is an arithmetic progression?

An arithmetic progression is a sequence of numbers where the difference between any two consecutive terms is constant. This difference is known as the common difference, and it can be either positive or negative.

How do you find the next term in an arithmetic progression?

To find the next term in an arithmetic progression, you need to add the common difference to the previous term. For example, if the common difference is 3 and the previous term is 10, the next term would be 13.

What is the formula for the nth term of an arithmetic progression?

The formula for the nth term of an arithmetic progression is a + (n-1)d, where a is the first term and d is the common difference. This formula can be used to find any term in the progression.

How do you find the sum of an arithmetic progression?

To find the sum of an arithmetic progression, you can use the formula Sn = n/2(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference. This formula can be used for both finite and infinite arithmetic progressions.

What is the significance of arithmetic progressions in mathematics?

Arithmetic progressions are essential in mathematics as they help to understand the concept of linear relationships and patterns. They are also used in various real-life situations, such as calculating interest rates, predicting population growth, and understanding the movement of objects in physics.

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