Question

numa PG temos a1= 1/3 e a7=243/64. determine a razão.

Answer 1

$\bullet \ a_n = a_1 \cdot q^{n - 1} \\\\ \circ a_7 = a_1 \cdot q^{6} \\\\ \frac{243}{64} = \frac{1}{3} \cdot q^{6} \\\\ \frac{243}{64} : \frac{1}{3} = q^6 \\\\ q^6 = \frac{243}{64} \cdot 3 \\\\ q^6 = \frac{729}{64} \\\\ q = \sqrt[6]{\frac{729}{64}} \\\\ q = \frac{\sqrt[6]{729}}{\sqrt[6]{64}} \\\\ \boxed{q = \frac{3}{2} = 1,5}$