Question

determine o décimo termo da PG (1/3,1,3,9...)

Answer 1

$\mathrm{PG=(1/3,1,3,9,\dots)}\\\\ \textbf{Raz\~ao:}\\\\ \mathrm{q=\dfrac{a_3}{a_2}=\dfrac{3}{1}\ \to\ \boxed{\mathrm{q=3}}}\\\\ \textbf{Termo geral:}\\\\ \mathrm{a_n=a_1.q^{n-1}\ \to\ a_n=\dfrac{1}{3}.3^{n-1}}\\\\ \mathrm{a_n=3^{n-1-1}\ \to\ \boxed{\mathrm{a_n=3^{n-2}}}}\\\\ \textbf{D\'ecimo termo:}\\\\ \mathrm{a_{10}=3^{10-2}\ \to\ a_{10}=3^8}\\\\ \boxed{\boxed{\mathbf{a_{10}=6561}}}$