Question

Progresia geometrică , vă rog frumos ajutați-mă !

Answer 1

Răspuns:

b4=b3*q

b3(1+q)= - 12 (1)

b9=b8*q

b8(1+q)=384 (2)

b3=b1*q^2

din 1 si 2

b8/b3 = - 384/12= - 32

b8=b1*q^7

b3=b1*q^2

b8/b3=q^5= - 32

q= - 2

Din (1)

b1*q*(1+q)= - 12

b1*(-2)*(-2+1)= - 12

b1= - 12/2= - 6

Answer 2

$\it b_3+b_4=-12 \Rightarrow b_3+b_3q=-12 \Rightarrow b_3(1+q)=-12\ \ \ \ \ (1)\\ \\ b_8+b_9\ =384 \Rightarrow \ b_8+b_8q=384 \Rightarrow \ b_8(1+q)=384\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow \dfrac{b_8(1+q)}{b_3(1+q)}=\dfrac{384}{-12} \Rightarrow \dfrac{b_8}{b_3}=-32 \Rightarrow \dfrac{b_3q^5}{b_3}=-32 \Rightarrow \\ \\ \\ \Rightarrow q^5=-32 \Rightarrow q^5=(-2)^5 \Rightarrow q=-2\ \ \ \ \ (3)$

$\it (1),\ (3) \Rightarrow b_3(1-2)=-12 \Rightarrow b_3\cdot(-1)=-12|_{\cdot(-1)} \Rightarrow b_3=12 \Rightarrow \\ \\ \Rightarrow b_1q^2=12 \Rightarrow b_1\cdot(-2)^2=12 \Rightarrow b_1\cdot4=12 \Rightarrow b_1=3$

Progresia geometrică este:

3,  -6,  12,  -24,...