Question

Найдите девятый член прогрессии(bn),если b1=100.000 и q=1/5

Answer 1

$b_1=100000\\\\ q= \frac{1}{5}\\\\ b_9-?$

$\boxed{b_n=b_1\cdot q^{n-1}}\\\\\\ b_9=100000\cdot( \frac{1}{5} )^{9-1}=100000\cdot (\frac{1}{5} )^8= \frac{10^5}{5^8}= \frac{(2\cdot5)^5}{5^8} = \frac{2^5\cdot5^5}{5^8}=\\\\ =2^5\cdot5^{5-8} =2^5\cdot5^{-3}= \frac{2^5}{5^3}= \frac{32}{125}=0,256$