Question

В геометрической прогрессии b1 = 16 , b2=8
Найдите : q , b6 , S5

Answer 1

$b _{1} =16 \\ b _{2} =8 \\ q= \frac{b _{2} }{b _{1} } = \frac{8}{16} = \frac{1}{2} \\ b _{6} =b ^{1} *q ^{5} =16* \frac{1}{32} = \frac{1}{2} \\ \\ S _{5} = \frac{b _{1} *(1-q ^{5} )}{1-q} = \frac{16*(1- \frac{1}{32}) }{1- \frac{1}{2} }= \frac{16*( \frac{32-1}{32}) }{ \frac{1}{2} } = \frac{16* \frac{31}{32} }{ \frac{1}{2} } = \frac{2*31}{ \frac{1}{2} } = \frac{62}{0.5 } =124$