3, b=-2...

June 2022 1 56 Report

Записать третий и четвёртый члены геометрической прогрессии, если:
1) b1=-8, b2=4
2) b1=-1/3, b2=-1
3) b1=-2/3, b=-2

Answers & Comments

Artem112

Verified answer

$b_n=b_1q^{n-1}; \ q= \frac{b_{n+1}}{b_n} = \frac{b_2}{b_1} 
\\\
b_3=b_1q^2=b_1\cdot( \frac{b_2}{b_1} )^2= \frac{b_2^2}{b_1} 
\\\
b_4=b_1q^3=b_1\cdot( \frac{b_2}{b_1} )^3= \frac{b_2^3}{b_1^2}$

$b_1=-8; \ b_2=4 \\\ b_3= \dfrac{b_2^2}{b_1}= \dfrac{4^2}{-8}=- \dfrac{16}{8} =-2 \\\ b_4= \dfrac{b_2^3}{b_1^2}=\dfrac{4^3}{(-8)^2}= \dfrac{2^6}{2^6} =1$

$b_1=- \dfrac{1}{3} ; \ b_2=-1 \\\ b_3= \dfrac{b_2^2}{b_1}= \dfrac{(-1)^2}{- \frac{1}{3} }=-3 \\\ b_4= \dfrac{b_2^3}{b_1^2}=\dfrac{(-1)^3}{(- \frac{1}{3} )^2}=- \dfrac{1}{1/9}} =-9$

$b_1=- \dfrac{2}{3} ; \ b_2=-2
\\\
b_3= \dfrac{b_2^2}{b_1}= \dfrac{(-2)^2}{- \frac{2}{3} }=- \dfrac{4}{2/3}= -6 
\\\
b_4= \dfrac{b_2^3}{b_1^2}=\dfrac{(-2)^3}{(- \frac{2}{3} )^2}=- \dfrac{8}{4/9} =-18$

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