Question

stie cineva? multumesc....

Answer 1

$\displaystyle a)a_1=-2,~a_8=12,~a_{10}=? \\ \\ a_8=12 \Rightarrow a_{8-1}+r=12 \Rightarrow a_7+r=12 \Rightarrow a_1+7r=12 \Rightarrow \\ \\ \Rightarrow -2+7r=12 \Rightarrow 7r=12+2 \Rightarrow 7r=14 \Rightarrow r= \frac{14}{7} \Rightarrow r=2 \\ \\ a_{10}=a_{10-1}+r=a_9+r=a_1+9r=-2+9 \cdot 2=-2+18=16 \\ \\ \boxed{a_{10}=16}$

$\displaystyle b)a_3=12,~a_6=30,~a_{10}=? \\ \\ a_3=12 \Rightarrow a_{3-1}+r=12 \Rightarrow a_2+r=12 \Rightarrow a_1+2r=12 \Rightarrow \\ \\ \Rightarrow a_1=12-2r \\ \\ a_6=30 \Rightarrow a_{6-1}+r=30 \Rightarrow a_5+r=30 \Rightarrow a_1+5r=30 \Rightarrow \\ \\ \Rightarrow 12-2r+5r=30 \Rightarrow -2r+5r=30-12 \Rightarrow 3r=18 \Rightarrow \\ \\ \Rghtarrow r= \frac{18}{3} \Rightarrow r=6 \\ \\ a_1=12-2 \cdot 6 \Rightarrow a_1=12-12 \Rightarrow a_1=0 \\ \\ a_{10}=a_{10-1}+r=a_9+r=a_1+9r=0+9 \cdot 6=54$

$\displaystyle \boxed{a_{10}=54}$