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\[ n = rac{-2 \pm \sqrt{4 + 840}}{2} \]
\[ n = rac{-2 \pm \sqrt{844}}{2} \]
\[ n = rac{-2 \pm 29}{2} \]
Prenons la racine positive :
\[ n = rac{27}{2} = 13.5 \]
Comme \( n \) doit être un entier, vérifions les erreurs ou ajustons. Re-résolvons :
\[ \sqrt{844} = 29 \]
\[ n = 13 \]
Vérifions :
\[ S_{13} = rac{13}{2}(6 + 24) = rac{13}{2} imes 30 = 195 \]