Question

Sa se gaseasca primul termen si ratia unei progresii geometrice, daca:

Answer 1

$\it a_2-a_1=-4 \Rightarrow a_1q-a_1=-4 \Rightarrow a_1(q-1) =-4\ \ \ (1)$

[tex]\it a_3-a_1=8 \Rightarrow a_1q^2-a_1=8 \Rightarrow a_1(q^2-1)=8 \Rightarrow \\\;\\ \Rightarrow a_1(q-1)(q+1) =8 \ \ \ (2)[/tex]

(1), (2) ⇒ -4(q+1) =8 ⇒ q+1 = -2 ⇒ q = -3     (3)

(1),  (3) ⇒ a₁(-3-1) =-4 ⇒ a₁·(-4) = -4 ⇒ a₁ = 1.