Question

Dada a progressão geométrica calcule o termo pedido (5,25,...) A9

Answer 1

$\textrm{P.G.:}\ \mathrm{(5,25,\dots)}\\\\ \mathrm{a_2=a_1q^{2-1}\ \to\ q=\dfrac{a_2}{a_1}\ \to\ q=\dfrac{25}{5}\ \to\ q=5}\\\\ \mathrm{a_9=a_1q^{9-1}\ \to\ a_9=a_1q^8\ \to\ a_9=5.5^8\ \to\ \boxed{\mathrm{a_9=5^9}}}$