Question

determine o primeiro termo da pg em que a4=27 e a7=125

Answer 1

$an=a1.q^{n-1}\\a4=27\\27=a1.q^{3}\\a7=125\\125=a1.q^6\\a1=\frac{27}{q^3}\\a1=\frac{125}{q^6}\\\\\frac{a1}{a1}=\frac{\frac{27}{q^3}}{\frac{125}{q^6}}$

$1=\frac{27q^3}{125}\\\\125=27q^3\\q^3=\frac{125}{27}\\q=\frac{ \sqrt[3]{125} }{ \sqrt[3]{27} }=\frac{5}{3}$

$an=a1.q^{n-1}\\a4=27\\27=a1.(\frac{5}{3})^3\\\\27=a1.\frac{125}{27}\\\\729=a1.125\\a1=\frac{729}{125}$