Question

106. Wyznacz iloraz ciągu geometrycznego (an), w którym a15 = 18, a a18 = −5 1/3.

Answer 1

[tex]a_{15}=18\\a_{18}=-5\frac{1}{3}\\\\a_{18}=a_{15}*q^{18-15}\\a_{18}=a_{15}*q^3\\-5\frac{1}{3}=18*q^3\ |:18\\-\frac{16}{3}*\frac{1}{18}=q^3\\-\frac{8}{3}*\frac{1}{9}=q^3\\-\frac{8}{27}=q^3\\q=\sqrt[3]{-\frac{8}{27}}\\q=-\frac{2}{3}[/tex]