Question

Fie $( a_{n}) _{n\ \textgreater \ 1}$ o progresie aritmetica. Stiind ca $a_{4} + a_{15} = 46$, sa se calculeze $a_{7} + a_{12}$.

Answer 1

[tex]a_4+a_{15}=46\\ a_1+3r+a_1+14r=46=\ \textgreater \ 2a_1+17r=46\\ a_7+a_{12}=a_1+6r+a_1+11r=2a_1+17r=46[/tex]

Answer 2

$a_4+a_{15}=46 \Rightarrow a_{4-1}+r+a_{15-1}+r=46\Rightarrow a_3+r+a_{14}+r=46 \Rightarrow \\ \Rightarrow a_1+3r+a_1+14r=46 \Rightarrow 2a_1+17r=46 \\ a_7+a_{12}= a_{7-1}+r+a_{12-1}+r=a_6+r+a_{11}+r= \\ =a_1+6r+a_1+11 r=2a_1+17r=46$