$a,\,a+d,\,a+2d,\,\cdots,\,a+(n-1)d$
어떤 수(첫 항, initial term, a)에서 시작하여 일정한 수(공차, common difference, d)를 차례로 더해서 만들어진 [[수열,sequence]]
$a_1=a,\,a_2=a+d,\,a_3=a+2d,\,\cdots,\,a_n=a+(n-1)d$

일반항(general term)
 $a_n=a+(n-1)d$

[[부분합,partial_sum]]
 $\sum_{k=1}^n a_k=\frac{n(2a+(n-1)d)}2$
 See [[등차수열의_합]]

[[등차중항]]

'''등차수열'''
 $a_n=pn+q$
의 [[생성함수,generating_function]]는
 $\frac{p}{1-x}+\frac{q}{(1-x)^2}$


= 다른 수열과의 관련 =
각 항의 역수가 '''등차수열'''인 수열은 [[조화수열,harmonic_sequence]].

= three arithmetic progression problem =
tmp via 2023's Biggest Breakthroughs in Math https://youtu.be/4HHUGnHcDQw?si=OTsekVU8UJIV4Ypy&t=861
{
Ggl:"three arithmetic progression problem"
1936 Paul_Erdos and Paul_Turan Ggl:"Paul Erdos Paul Turan"
1946 Felix_Behrend
1653 Klaus_Roth
Ggl:"Roth-Meshulam proof"
sifting
Ggl:"Strong Bounds for 3-Progressions"
}

= arithmetic progression topology =
arithmetic_progression_topology
WpEn:Arithmetic_progression_topologies
Ggl:"arithmetic progression topology"

----
'''arithmetic(arithmetical) sequence(progression)'''

https://encyclopediaofmath.org/wiki/Arithmetic_progression

Up: [[수열,sequence]]