Question

qual e a soma dos infinito termos da PG (50,10,2,)

Answer 1

Dados:

$\mathsf{a_{1}=50}\\\mathsf{q=\dfrac{a_{2}}{a_{1}}=\dfrac{10}{50}=\dfrac{1}{5}}$

Solução

$\mathsf{S_{n}=\dfrac{a_{1}}{1-q}}\\\mathsf{S_{n}=\dfrac{50}{1-\frac{1}{5}}}\\\mathsf{S_{n}=\dfrac{50}{\frac{5-1}{5}}}$

$\mathsf{S_{n}=\dfrac{50}{\frac{4}{5}}}\\\mathsf{S_{n}=50.\dfrac{5}{4}}\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{S_{n}=\dfrac{125}{2}}}}}}$