Explicatii:
La primul raspuns corect primeste 200 Lei
La al 2-lea raspuns corect tripleaza suma: 200 × 3
La al 3-lea raspuns corect tripleaza suma: 200 × 3 × 3
- - - - - - - - - - - -
La al n-lea raspuns corect tripleaza suma: 200 × 3 × 3 ... × 3
.
[tex]\displaystyle\bf\\Suma~totala~incasata~este:\\\\S=200\times3^n\\\\Numarul~de~raspunsuri~corecte~este:\\\\RC =1+n\\1~raspuns~este~primul~pentru~care~a~primit~200~lei\\n~raspunsuri~sunt~cele~care~au~triplat~suma.\\\\Rezolvare:\\\\437400=200\times3^n\\\\3^n=\frac{437400}{200}=\frac{4374}{2}=2187\\\\3^n=2187\\\\2187=81\times27=3^4\times3^3=3^{4+3}=3^7\\3^n=3^7\\\boxed{\bf n=7}\\437400=200\times3^7\\Raspunsuri~corecte:\\\boxed{\bf RC=1+7=8~raspunsuri~corecte}[/tex]
