[tex]a) \hbox{Sirul este o progresie aritmetica avand ratia r=3} \\\\ r=a_2-a_1 =20-17 \longrightarrow \underline{r=3} \\\\ \\ \hbox{Regula de formare a sirului este exact formula pentru termenul general }\\\hbox{al progresiei aritmetice:} \\\\ \boxed{a_n=a_1+(n-1)*r} \\\\\\ b)a_{96}=a_1+(96-1)*r \\\\ a_{96}=17+95*3=17+285 \\\\ \boxed{a_{96}\to 302} \\\\\\ c) 464=a_1+(n-1)*3 \\\\ 464-17=(n-1)*3 \\\\ 447=(n-1)*3 \ \ \ |:3 \\\\ 149=n-1 \\\\ \boxed{n=150} \\\\ \hbox{Da,464 este termenul cu numarul 150 din sir.} [/tex]
[tex]d)S=17+20+23+...+464 \\\\ S= \frac{a_1+a_n}{2}*n \\\\ S_{150}=\frac{17+464}{\not2}*\not 150 \\\\ S_{150}= 481*75 \\\\ \boxed{S_{150}=36075}[/tex]
