Question

numa PA, o valor do decimo terceiro termo é 0,01 e o termo seguinte é 2/3. determine o nonagésimo quinto termo

Answer 1

$a_{13}=0,01=a_{13}=\frac{1}{100}\\\\a_{14}=\frac{2}{3}\\\\r=\frac{2}{3}-\frac{1}{100}\\\\r=\frac{200}{300}-\frac{3}{300}\\\\r=\frac{197}{300}\\\\\frac{2}{3}=a_{1}+13.\frac{197}{300}\\\\a_{1}=\frac{2}{3}-\frac{2.561}{300}\\\\a_{1}=\frac{200}{300}-\frac{2.561}{300}\\\\a_{1}=\frac{2.361}{300}\\\\a_{95}=-\frac{2.361}{300}+(95-1).\frac{197}{300}\\\\a_{95}=-\frac{2.361}{300}+\frac{18.518}{300}\\\\a_{95}=\frac{16.157}{300}$