Question

Given the formula, Sn=a1−r^n over 1−r, what is the sum of the first nine terms of the geometric series: 324, -108, 36, -12...

If necessary, round to the hundredths place. (2 places after the decimal)

Answer 1

≈ 486.02

Explanation:

The sum to n terms of a geometric series is

`S_(n)` =
`(a(1-r^(n)) )/(1-r)`

where a is the first term and r the common ratio

Here a = 324 and r =
`(-108)/(324)` = -
`(1)/(3)`, thus

`S_(9)` =
`(324(1-(-1/3)^9))/(1-(1)/(3) )`

=
`(324(1+(1)/(19683)) )/((2)/(3) )`

= 486(
`(19684)/(19683)` ) ≈ 486.02 ( to the nearest hundredth )