Question

Intro progresie aritmetica a2016=2*a1016
a16=?

Answer 1

[tex]\it a_{2016} = 2a_{1016} \ \ \ (1) \\\;\\ a_{2016} = a_{16} +2000r \ \ \ \ (2) \\\;\\ a_{1016} =a_{16} +1000r\ \ \ \ (3) [/tex]

[tex]\it (1),\ (2),\ (3) \Rightarrow a_{16} +2000r = 2(a_{16} +1000r) \Rightarrow \\\;\\ \Rightarrow a_{16} +2000r = 2a_{16} +2000r \Rightarrow 2000r-2000r=2a_{16}-a_{16} \Rightarrow \\\;\\ \Rightarrow 0=a_{16} \Rightarrow a_{16} = 0[/tex]