Witaj. Zadanie 1. [latex] left { {{a_{4}=-40} atop {a_{9}=1280}} ight. \\ left { {{a_{1}cdot q^{3}=-40 => a_{1}=frac{-40}{q^{3}}} atop {a_{1}cdot q^{8}=1280}} ight. \-----------\\frac{-40}{q^{3}}cdot q^{8}=1280\\-40q^{5}=1280\\q^{5}=-32\\q=-2[/latex] [latex] left { {{a_{1}=frac{1280}{(-2)^{8}}} atop {q=-2}} ight. \\ left { {{a_{1}=5} atop {q=-2}} ight. [/latex] Mamy więc ciąg geometryczny: [latex]a_{n}=a_{1}cdot q^{n-1}\\a_{n}=5cdot(-2)^{n-1}[/latex] Zadanie 2. [latex](2, (x-1), (x+1))[/latex] - ciąg geometryczny [latex]frac{x+1}{x-1}=frac{x-1}{2} | x-1 eq0 => x eq1\\2(x+1)=(x-1)^{2}\\2x+2=x^{2}-2x+1\\x^{2}-4x-1=0\\Delta=(-4)^{2}-4cdot1cdot(-1)=16+4=20 sqrt{Delta}=sqrt{20}=2sqrt{5}\\x_{1}=frac{2sqrt{5}+4}{2}=sqrt{5}+2 lub x_{2}=frac{-2sqrt{5}+4}{2}=-sqrt{5}+2[/latex]
