Question

xn геометрическая программа q=√3,Xn=18√3,Sn=26√3+24 найти x,n
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Answer 1

$q=\sqrt{3}\\\\x_{n}=18\sqrt{3}\\\\S_{n}=26\sqrt{3}+24\\\\\\S_{n} =\frac{x_{n}q-x_{1}}{q-1}\\\\26\sqrt{3}+24=\frac{18\sqrt{3}*\sqrt{3}-x_{1}}{\sqrt{3}-1 }\\\\26\sqrt{3}+24=\frac{54-x_{1}}{\sqrt{3}-1 }\\\\(26\sqrt{3}+24)*(\sqrt{3} -1)=54-x_{1}\\\\78-26\sqrt{3}+24\sqrt{3} -24=54-x_{1}\\\\54-2\sqrt{3}=54-x_{1}\\\\\boxed{x_{1}=2\sqrt{3}} \\\\\\x_{n}=x_{1}*q^{n-1}\\\\18\sqrt{3}=2\sqrt{3}*(\sqrt{3})^{n-1}\\\\(\sqrt{3})^{n-1}=\frac{18\sqrt{3}}{2\sqrt{3}}$

$(\sqrt{3})^{n-1}=9\\\\(\sqrt{3})^{n-1}=(\sqrt{3})^{4}\\\\n-1=4\\\\\boxed{n=5}$