Question

Doar a și f, vă rog frumos!!Dau coroana!!!​

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

a)

$\bf a_4=10\ \ \ \ \ (1)\\ \\ a_6-3a_2=4 \Rightarrow a_4+2r-3(a_4-2r)=4\Rightarrow a_4+2r-3a_4+6r=4\Rightarrow \\ \\ \Rightarrow 8r-2a_4=4\ \stackrel{(1)}{\Longrightarrow}\ 8r-20=4\Big|_{+20}\Rightarrow 8r=24\Big|_{:8}\Rightarrow r=3\ \ \ \ \ \ (2)\\ \\ a_4=10\Rightarrow a_1+3r=10\ \stackrel{(2)}{\Longrightarrow}a_1+9=10\Rightarrow a_1=1$

f)

$\bf a_2+a_3=8 \Rightarrow a_2+a_2+r=8 \Rightarrow 2a_2+r=8 \Rightarrow 2a_2=8-r\ \ \ \ \ (1)\\ \\ a_2^2-a_1^2=8 \Rightarrow (a_2-a_1)(a_2+a_1)=8 \Rightarrow r(a_2+a_2-r)=8 \Rightarrow \\ \\ \Rightarrow r(2a_2-r)=8\ \stackrel{(1)}{\Longrightarrow}\ r(8-r-r)=8 \Rightarrow r(8-2r)=8 \Rightarrow \\ \\ \Rightarrow 2r(4-r)=8\ \Big|_{:2} \Rightarrow r(4-r)=4 \Rightarrow 4r-r^2=4 \Rightarrow 0=r^2-4r+4 \Rightarrow \\ \\ \Rightarrow r^2-4r+4=0 \Rightarrow (r-2)^2=0 \Rightarrow r=2\ \ \ \ \ \ (2)$

$\bf (1),\ (2) \Rightarrow 2a_2=8-2 \Rightarrow 2a_2=6 \Rightarrow a_2=3 \Rightarrow a_1+r=3 \Rightarrow \\ \\ \\ \Rightarrow a_1+2=3 \Rightarrow a_1=1$