Question

a1= -1
a5= 7
Calculati a2012=? ( progresii aritmetice )

Answer 1

[tex] \left \{ {{a_1=a_0+r} \atop {a_5=a_0+5\cdot r}} \right. \Leftrightarrow \left \{ {{-1=a_0+r} \atop {7=a_0+5\cdot r}} \right. \Leftrightarrow \left \{ {{a_0=-1-r} \atop {7=-1-r+5\cdot r}} \Leftrightarrow \left \{ {{a_0=-1-r} \atop {8=4\cdot r}} \\[/tex]
[tex]\Leftrightarrow \left \{ {{a_0=-1-r} \atop {r=2}} \Leftrightarrow \left \{ {{a_0=-1-2} \atop {r=2}} \Leftrightarrow \left \{ {{a_0=-3} \atop {r=2}} \\[/tex]
[tex]a_{2012}=a_0+2012\cdot r=-3+2012\cdot 2=-3+4024=4021\\ \underline{a_{2012}=4021}[/tex]