Respuesta :
Answer:
[tex]a_{7}[/tex] = [tex]\frac{729}{4096}[/tex]
Step-by-step explanation:
To obtain the next term in the sequence multiply the previous term by - [tex]\frac{3}{4}[/tex]
given [tex]a_{3}[/tex] = [tex]\frac{9}{16}[/tex], then
[tex]a_{4}[/tex] = - [tex]\frac{3}{4}[/tex] × [tex]\frac{9}{16}[/tex] = - [tex]\frac{27}{64}[/tex]
[tex]a_{5}[/tex] = - [tex]\frac{3}{4}[/tex] × - [tex]\frac{27}{64}[/tex] = [tex]\frac{81}{256}[/tex]
[tex]a_{6}[/tex] = - [tex]\frac{3}{4}[/tex] × [tex]\frac{81}{256}[/tex] = - [tex]\frac{243}{1024}[/tex]
[tex]a_{7}[/tex] = - [tex]\frac{3}{4}[/tex] × - [tex]\frac{243}{1024}[/tex] = [tex]\frac{729}{4096}[/tex]
