Question

Aflati ratia unei progresii aritmetice daca a2=5, a3=9.

Answer 1

a3=a2+r
9=5+r
r=9-5
r=4

Answer 2

$\displaystyle a_2=5,~a_3=9,~r=? \\ a_2=5 \Rightarrow a_{2-1}+r=5 \Rightarrow a_1+r=5 \Rightarrow a_1=5-r \\ a_3=9 \Rightarrow a_{3-1}+r=9 \Rightarrow a_2+r=9 \Rightarrow a_1+2r=9 \Rightarrow \\ \Rightarrow 5-r+2r=9 \Rightarrow -r+2r=9-5 \Rightarrow \boxed{r=4 }$