Answer:
[tex]\frac{463}{3}[/tex]
Step-by-step explanation:
The given geometric series is:
243-162+108.....+64/3
The first term is [tex]a=243[/tex].
The common ratio is:
[tex]r=\frac{-162}{243}=-\frac{2}{3}[/tex]
The sequence is finite, so we can generate all the terms by repeatedly multiplying by the common ratio until we get to the last term.
The complete series is
243-162+108-72+48-32+64/3
The sum is:
[tex]243+108+48+64/3-162-72-32=\frac{463}{3}[/tex]
