[tex]\displaystyle\bf\\E2)\\Se~da~progresia~aritmetica\!:~~~x,~y,~-21,~z,~-15,~t,~...\\Se~cere\!:~~~sa~se~determine~termenuii~~x,~y,~z,~t\\\\Rezolvare:\\\\Aflam~ratia.\\\\z=-21+r~~si~~-15=z+r\\\\\implies~~-15=-21+2r\\\\2r=-15+21\\\\r=\frac{-15+21}{2}=\frac{6}{2}=3\\\\\boxed{\bf r=3}\\\\t=-15+3=-12\\z=-21+3=-18\\y=-21-3=-24\\x=y-3=-24-3=-27[/tex]
.
[tex]\displaystyle\bf\\E3)\\\\\\a)\\r=\frac{a_8-a_1}{8-1}=\frac{12-(-2)}{8-1}=\frac{12+2}{8-1}=\frac{14}{7}=2\\\\a_{10}=a_8+r(10-8)=12+2(10-8)=12+2\times2=12+4=16\\\\\\b)\\\\r=\frac{a_6-a_3}{6-3}=\frac{30-12}{6-3}=\frac{18}{3}=6\\\\a_{10}=a_6+r(10-6)=30+6(10-6)=30+6\times4=30+24=54[/tex]
