|
|
|
|
arithmetic progression
|
(Definition)
|
|
|
Arithmetic progression of length  , initial term  and common difference  is the sequence
 .
The sum of terms of an arithmetic progression can be computed using Gauss's trick:
![$\textstyle \parbox{\linewidth}{\begin{align*} S&=\makebox[7em]{$(a_1+0)$}+\make... ...b+\makebox[7em]{$(2a_1+(n-1)d)$}+ \makebox[7em]{$(2a_1+(n-1)d)$}. \end{align*}}$](http://images.planetmath.org:8080/cache/objects/4302/l2h/img5.png "$\textstyle \parbox{\linewidth}{\begin{align*} S&=\makebox[7em]{$(a_1+0)$}+\make... ...b+\makebox[7em]{$(2a_1+(n-1)d)$}+ \makebox[7em]{$(2a_1+(n-1)d)$}. \end{align*}}$")
We just add the sum with itself written backwards, and the sum of each of the columns equals to
 . The sum is then
|
"arithmetic progression" is owned by bbukh.
|
|
(view preamble)
Cross-references: Gauss', sum, sequence, difference, term, length
There are 6 references to this entry.
This is version 7 of arithmetic progression, born on 2003-05-26, modified 2004-09-24.
Object id is 4302, canonical name is ArithmeticProgression.
Accessed 16764 times total.
Classification:
| AMS MSC: | 00A05 (General :: General and miscellaneous specific topics :: General mathematics) | | | 11B25 (Number theory :: Sequences and sets :: Arithmetic progressions) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|
