Zad1.  Wyznacz wzór ogólny monotonicznego ciągu geometrycznego  [latex] left { {{a6= -4} atop {a10= -1/64} ight. [/latex]

[latex]\a_6*q^4=a_{10} \ \q^4=-frac{1}{64}:(-4)=frac{1}{4^3*4}=(frac14)^4 \ \q=frac14 \ \a_1*(frac14)^5=-4 \ \a_1=-4*4^5=-4^6 \ \a_n=a_1*q^{n-1} \ \a_n=-4^6*(frac14)^{n-1}=-4^7*(frac14)^n[/latex]

[latex]a_n = a_1 * q^{n-1} \ a_6 = -4 \ a_1 * q^5 = -4 \ a_1 * q^9 = - frac{1}{64} \ q^{-4} = 256 \ frac{1}{q^4} = 256 \ 256 * q^4 = 1 \ q^4 = frac{1}{256} \ q = frac{1}{4} \ a_1 * frac{1}{1024} = -4 \ a_1 = -4096 \ a_n = -4096 * frac{1}{4}^{n-1} [/latex]