Question

progresie geometrica b1=10 bn+1=1/5*bn care este formula termenului general bn?

Answer 1

$b_2=\dfrac{1}{5}\cdot b_1\\\\b_3=\dfrac{1}{5}\cdot b_2\\\\b_4=\dfrac{1}{5}\cdot b_3\\\ldots\\b_{n}=\dfrac{1}{5}\cdot b_{n-1}\\b_{n+1}=\dfrac{1}{5}\cdot b_n.~Dup\breve{a}\;inmul\c{t}ire\;membru\;cu\;membru\Rightarrow\\ \Rightarrow (b_2\cdot b_3\cdot b_4\cdot\ldots\cdot b_n)\cdot b_{n+1}=\dfrac{1}{5^n}\cdot b_1\cdot (b_2\cdot b_3\cdot\ldots\cdot b_{n-1}\cdot b_{n})\\b_{n+1}=\dfrac{b_1}{5^n}\Rightarrow b_n=\dfrac{10}{5^{n-1}},\;n\geqslant 1.$

Green eyes.