Voi mai considera sirul:
Linia 1: 1
Linia 2: 2 3
Linia 3: 3 4 5
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[tex]Notand~cu~a_n~al~n-lea~termen~al~sirului~din~enunt,~iar \\ \\ cu~b_n~al~n-lea~termen~din~sirul~meu,~avem~ca~a_n=2(b_n-1) \\ \\ In~sirul~meu~putem~observa~ca~ultimul~numar~de~pe~linia~k \\ \\ este~1+2+...+k= \frac{k(k+1)}{2}. \\ \\ Daca~ \frac{k(k+1)}{2}~este~ultimul~termen~de~pe~linia~k,~inseamna~ca~ \\ \\ urmatorul~termen~(adica~ \frac{k(k+1)}{2}+1)~este~primul~termen~din~ \\ \\ linia~k+1. [/tex]
[tex]Ultimul~termen~din~linia~k-1~este~ \frac{(k-1)k}{2},~deci~primul~ \\ \\ termen~din~linia~k~este~ \frac{(k-1)k}{2}+1.~Deci~acum~putem~scrie: \\ \\ Linia~k:~ \frac{(k-1)k}{2}+1~ ;~\frac{(k-1)k}{2}+2 ~;~ ... ~;~ \frac{k(k+1)}{2}. \\ \\ Deci~primul~numar~de~pe~linia~157~al~sirului~meu~este~12246, \\ \\ iar~ultimul~12403. [/tex]
[tex]Primul~numar~de~pe~linia~157~din~sirul~din~enunt~este,~deci, \\ \\ 2 \cdot 12245,~ultimul~fiind~2 \cdot 12402. \\ \\ Precizez~ca~n,k \in N^*,~iar~k \geq 2.[/tex]
