Question

exercitiul 35
a3 = 11
a11= 3
a7 = ?

Answer 1

Notez ratia cu r:
a₃=11 => a₁+2r=11
a₁₁=3  => a₁+10r=3
Scazand se obtine: 
-8r=8  => r=-1
 a₇=a₃+4r
a₇=11-4 = 7

Answer 2

[tex] \left\{ \begin{array}{ll} a_3= 11 \\ a_{11} = 3 \\ a_7 = a_1+6r\end{array} \right \Rightarrow \left\{ \begin{array}{ll} a_1+2r= 11 \\ a_{1}+10r = 3 \\ a_7 = a_1+6r\Big|\cdot 2\end{array} \right \Rightarrow \\ \\ \Rightarrow \left\{ \begin{array}{ll} \left \begin{array}{ll} a_1+2r=11 \\ a_1+10r=3 \end{array} \right|(+) \\ 2a_7 = 2a_1+12r\end{array} \right \Rightarrow \left\{ \begin{array}{ll} 2a+12r = 14\\ 2a_7 = 14 \end{array} \right| \Rightarrow \boxed{a_7 = 7}[/tex]