Question

What is the sum of the geometric series 243-162+108.....+64/3

Answer 1

`(463)/(3)`

Explanation:

The given geometric series is:

243-162+108.....+64/3

The first term is
`a=243`.

The common ratio is:

`r=(-162)/(243)=-(2)/(3)`

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:

`243+108+48+64/3-162-72-32=(463)/(3)`