Question

fie (bn) o progresie geometrica pozitivă. Stiind ca b1=1 si b2017=9*b2017, determinați b2015. .

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Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

 

$\displaystyle\bf\\b_1=1\\\\b_{2017}=9\times b_{2013}\\\\2017-2013=4\\\\b_{2017}=q^4\times b_{2013}\\\\\text{\bf~unde q este ratia progresiei geometrice}\\\\q^4=9\\\\q=\sqrt[\b4]{9}\\\\\boxed{\bf~q=\sqrt{3}}\\\\b_1=1\\\\b_{2015}=?\\\\2015-1=2014\\\\b_{2015}=q^{2014}\times b_1\\\\b_{2015}=\Big(\sqrt{3}\Big)^{2014}\times 1\\\\b_{2015}=\Big(\sqrt{3}\Big)^{2\times1007}\\\\b_{2015}=\left[\Big(\sqrt{3}\Big)^2\right]^{1007}\\\\\boxed{\bf~b_{2015}=3^{1007}}$