Question

Calcule a soma das 7 primeiras PG ,8 ,4 ,2, 1 , 1/2

Answer 1

Precisamos primeiro achar a razão da PG:

           $Razao=\frac{a_{n+1}}{a_n}\\\\\\Razao=\frac{a_2}{a_1}\\\\\\Razao=\frac{4}{8}\\\\\\Razao=\frac{1}{2}$

Agora podemos utilizar a equação da soma dos termos finitos da PG:

           $S_n=\frac{a_1.(q^n-1)}{q-1}\\\\\\S_7=\frac{8.\left(\left(\frac{1}{2}\right)^7-q\right)}{\frac{1}{2}-1}\\\\\\S_7=\frac{8.\left(\frac{1}{2^7}\right)-1}{-\frac{1}{2}}\\\\\\S_7=\frac{8.\left(\frac{1}{128}-1\right)}{-\frac{1}{2}}\\\\\\S_7=\frac{8\left(-\frac{127}{128}\right)}{-\frac{1}{2}}\\\\\\S_7=\frac{-\frac{127}{16}}{-\frac{1}{2}}\\\\\\S_7=\frac{127\,.\,2}{16}\\\\\\S_7=\frac{127}{8}$