Talk:Arithmetic progression

message: According to Mathworld, which has a link in the article, an arithmetic series is the sum of an arithmetic progression or sequence.  Charles Matthews has obscured this distinction by redirecting arithmetic series to arithmetic progression.  I'm not sure whether the distinction made by Mathworld is commonly recognised by mathematicians, so I'm not going to revert the change.  I'll wait for comments.  -- Heron 15:12, 7 Mar 2004 (UTC)
replies: text: The redirect only implies that information on arithmetic series is contained in the arithmetic progression article, not that the two terms are synonymous. The article is quite clear on the latter point (and mathworld is right, of course). -- Arvindn 15:39, 7 Mar 2004 (UTC)

text: I strongly think arithmetic series should be merged back into this article. Fredrik | talk 14:20, 19 August 2005 (UTC)
replies: text:  Fredrik, thanks! Oleg Alexandrov 19:35, 20 August 2005 (UTC)
replies: text:  No problem :) - Fredrik | talk 19:38, 20 August 2005 (UTC)

text: Does this have anything to do with the contents of our article on arithmetic progressions? If not, it shouldn't be here. —David Eppstein (talk) 19:02, 16 September 2010 (UTC)
thread_title: Merging with [[arithmetic series]]

message: :I think this would be useful to add under 1 Sum (arithmetic series)
===Sum of Sines===
The arguments of a sum of sines can be in arithmetic progression, as follows
:S=\sin \varphi + \sin {(\varphi + \alpha)} + \cdots + \sin {(\varphi + n\alpha)}.
It has also, like a normal arithmetic sequence, a concise formula, written as
:S=\frac{\sin{(\frac{(n+1) \alpha}{2})} \cdot \sin{(\varphi + \frac{n \alpha}{2})}}{\sin{\frac{\alpha}{2}}}.
===Sum of Cosines===
Analogous to the sum of sines with their arguments in arithmetic sequence, there is also one with cosines:
:S=\cos \varphi + \cos {(\varphi + \alpha)} + \cdots + \cos {(\varphi + n\alpha)}.
There is also, the general expression, which is somewhat similar to the one of the sines:
:S=\frac{\sin{(\frac{(n+1) \alpha}{2})} \cdot \sin{(\varphi + \frac{n \alpha}{2})}}{\sin{\frac{\alpha}{2}}}
:S=\frac{\sin{\frac{(n+1) \alpha}{2}} \cdot \cos{(\varphi + \frac{n \alpha}{2})}}{\sin{\frac{\alpha}{2}}}.
:In response to the unsigned material above: I think this material represents a "trigonometric progression" and not an "arithmetic progression". Maybe there is someplace it can be placed in the trigonometry articles. Thelema418 (talk) 05:06, 23 August 2012 (UTC)
thread_title:  sum of sine and cosine in arithmetic progression 

message: Analogous to the sum of sines with their arguments in arithmetic sequence, there is also one with cosines:
:S=\cos \varphi + \cos {(\varphi + \alpha)} + \cdots + \cos {(\varphi + n\alpha)}.
There is also, the general expression, which is somewhat similar to the one of the sines:
:S=\frac{\sin{(\frac{(n+1) \alpha}{2})} \cdot \sin{(\varphi + \frac{n \alpha}{2})}}{\sin{\frac{\alpha}{2}}}
:S=\frac{\sin{\frac{(n+1) \alpha}{2}} \cdot \cos{(\varphi + \frac{n \alpha}{2})}}{\sin{\frac{\alpha}{2}}}.
:In response to the unsigned material above: I think this material represents a "trigonometric progression" and not an "arithmetic progression". Maybe there is someplace it can be placed in the trigonometry articles. Thelema418 (talk) 05:06, 23 August 2012 (UTC)
thread_title: Sum of Cosines

message: For history of AP in old Indian texts, see this research paper.--Nizil (talk) 20:10, 1 January 2017 (UTC)
replies: text: If the article is going to cover history at all, it should also mention Archimedes, who proved an equivalent formula for the sum of an arithmetic progression as a part of his more difficult proof of the sum of the squares of the terms of the progression, in his treatise 'On Conoids and Spheroids' (around 300 BC).  This is mentioned in T. L. Heath's edition.  I would guess that the formula was also known in some form to the Arab mathematicians, but I have not researched the history of the subject in depth.109.150.6.229 (talk) 19:52, 19 March 2019 (UTC)
thread_title:  History 

message: There needs to be a separate article named common difference of an arithmetic progression.  Huzaifa abedeen (talk) 05:14, 1 October 2020 (UTC)
thread_title:  common difference 

message: I've trimmed a moderate amount from this article, culling stuff like bullet points that restate the obvious and look like they were copied out of a study guide for a junior-high quiz, and a "section" devoted to two lines of Python. Wikipedia is not a textbook, a cheat sheet for elementary formulae, or a Programming 101 manual. In addition, claims like  are blatantly unhistorical and even make the article self-contradictory. Pop-math wiki websites and random study guides are not sources we should depend upon, particularly when standard texts and peer-reviewed papers on the history of mathematics are plentiful. XOR'easter (talk) 20:03, 29 October 2020 (UTC)
replies: text: Please consider adding common difference d, general form of an AP a, a + d, a + 2d, a + 3d, . . ., general term of an AP a_n, middle term of an AP, and Arithmetic mean. Huzaifa abedeen (talk) 05:42, 31 October 2020 (UTC)
thread_title:  Removals 

message: Formula 118.103.138.107 (talk) 06:00, 29 December 2021 (UTC)
thread_title:  Math