Răspuns:
Explicație pas cu pas: Fie a1=22,a2=23.....Observam ca putem scrie:
a1=22;
a2=a1+1
a3=a2+2
a4=a3+3
a5=a4+4
.....
an=an-1+(n-1)
----------------------
a1+a2+a3+....+an-1+an=22+(a1+1)+(a2+2)+...+[an-1+(n-1)]
(a1+a2+a3+...+an-1)+an=22+[1+2+...+(n-1])+(a1+a2+...+an-1)⇒
an=22+[n(n-1)]/2
n=2009⇒a2009=22+(2009·2008)/2=22+2009·1004=2017058
