Question

матеша геометрическая прогрессия ​

Answer 1

1.

$b_{1} = \frac{1}{2}\\b_{2} = -\frac{1}{6}\\q = \frac{b_{2}}{b_{1}} = \frac{-\frac{1}{6}}{\frac{1}{2}} = -\frac{1}{3}\\b_{n} = b_{1}*q^{n-1}\\b_{n} = \frac{1}{2}*(-\frac{1}{3})^{n-1}$

2.

$b_{1} = 21\\q = \frac{1}{5}\\b_{n} = b_{1}*q^{n-1}\\b_{3} = b_{1}*q^{2} = 21*\frac{1}{25} = \frac{21}{25} = 0,84$

3.

$x_{3} = -125\\q = -5\\x_{3} = x_{1}*q^{2}\\x_{1} = \frac{x_{3}}{q^{2}} = \frac{-125}{25} = -5$

4.

$b_{4} = \frac{1}{16}\\b_{5} = \frac{1}{32}\\q = \frac{b_{5}}{b_{4}} = \frac{\frac{1}{32}}{\frac{1}{16}} = \frac{1}{2}\\\\b_{4} = b_{2}*q^{2}\\b_{2} = \frac{b_{4}}{q^{2}} = \frac{\frac{1}{16}}{\frac{1}{4}} = \frac{1}{4}$