A.P.即係咩?

arithmetic progression or arithmetic sequence
If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:


圖片參考：http://upload.wikimedia.org/math/0/2/9/029db8d36d83883674e157f930cf479d.png

Sum (arithmetic series)
The sum of the components of an arithmetic progression is called an arithmetic series. The formula for the sum of the first n terms of an arithmetic progression is:


圖片參考：http://upload.wikimedia.org/math/9/a/5/9a5fb55b3d24acaa271a9e4eea85cd83.png

This formula is derived from the fact that the sum of the first and the last term is the same as the sum of the second and the second last, and so forth. An often-told story is that Carl Friedrich Gauss discovered it when his third grade teacher asked the class to find the sum of the first 100 numbers, and he instantly computed the answer (5050).
Proof:

圖片參考：http://upload.wikimedia.org/math/3/6/1/361f802d906ec5570850c5d0a3e28b47.png


圖片參考：http://upload.wikimedia.org/math/3/3/d/33d97349f33ca351fc8eafedc14f125d.png


圖片參考：http://upload.wikimedia.org/math/1/2/2/122f1a6e41cb9737b9ffee4e154bae43.png


圖片參考：http://upload.wikimedia.org/math/1/3/4/134fa4927dc3bef1cd63f89449590a13.png
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