Odd-Numbered Arithmetic Progressions: A Different Perspective

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In summary, the conversation discusses a method for taking three terms in an arithmetic progression (AP) as a-d, a, a+d. It also mentions a general method for taking (2r+1) terms in an AP as a-rd, a-(r-1)d, ..., a-d, a, a+d, with 'r' being an integer related to the total number of terms in the sequence. The context of this discussion is unclear and it is not clear what the purpose of counting an AP with an odd number of terms in this manner is.
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Kartik.
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"If we have to take three terms in an AP, it is convenient ti take them as a-d,a,a+d. In general, we take a-rd,a-(r-1)d,...,a-d,a,a+d, in case we have to take (2r+1) terms in an AP."

What do they mean by the portion in bold?
What is 'r' here ?
 
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r is an integer related to the total number of terms in the sequence (2r+1). I am not aware of the context.

The author (for some reason) is counting an arithmetic progression with an odd number of terms by starting in the middle and counting r terms in each direction. I have no idea what the point is. Usually a discussion of AP will start with the first term, while the number of terms may be odd or even.
 

Related to Odd-Numbered Arithmetic Progressions: A Different Perspective

What is the definition of "Progressive terms assumption"?

Progressive terms assumption is a statistical assumption in which the probability of an event or outcome increases as time goes on. It is often used in analyzing longitudinal data or data collected over a period of time.

How is "Progressive terms assumption" different from "Stationary terms assumption"?

The main difference between these two assumptions is the concept of time. While progressive terms assumption assumes that the probability of an event changes over time, stationary terms assumption assumes that the probability remains constant over time.

Why is "Progressive terms assumption" important in statistical analysis?

Progressive terms assumption is important because it allows for the analysis of data that changes over time. Without this assumption, the results of statistical analysis may not accurately reflect the underlying trends in the data.

What are some common methods for testing "Progressive terms assumption"?

There are several methods for testing progressive terms assumption, including graphical methods such as plotting the data over time and looking for patterns, and statistical tests such as the Durbin-Watson test and the Breusch-Godfrey test.

Can "Progressive terms assumption" be violated?

Yes, progressive terms assumption can be violated. This can occur when the probability of an event does not actually increase over time, or when there are other underlying trends or patterns in the data that are not accounted for. It is important to carefully assess the data and choose appropriate methods for analysis to ensure that this assumption is not violated.

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