Question

Find the sum of the first 9 terms
of the geometric sequence: 0.5, 1, 2,-..

Answer 1

S₉ = 255.5

Explanation:

the sum to n terms of a geometric sequence is

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

where a₁ is the first term and r the common ratio

here a₁ = 0.5 and r =
`(a_(2) )/(a_(1) )` =
`(1)/(0.5)` = 2 , then

S₉ =
`(0.5(2^(9)-1) )/(2-1)`

=
`(0.5(512-1))/(1)`

= 0.5(511)

= 255.5