Find the sum of the first 12 terms of this sequence:

9,4.5,2.25,...

I believe that the pattern is dividing the term by 2,and I keep getting 7.9956 for the sum, but that is incorrect.
Anyone understand this?

4 answers

I might be wrong, but i got 17.99121094.
I just calculated again and got that. Thank you!
Geometric Sequences :

xn = a * r ^ ( n - 1 )

In this case :

a = 9 , r = 1 / 2

xn = a * ( 1 / 2 ) ^ ( n - 1 )

Sum:

S = a ( 1 - r ^ n ) / ( 1 - r )

a = 9 , r = 1 /8 2 , n = 12 so :

S = 9 * [ 1 - ( 1 / 2 ) ^ 12 ] / ( 1 - 1 / 2 ) =

9 * ( 1 - 1 / 4096 ) / ( 1 / 2 ) =

2 * 9 * ( 4096 / 4096 - 1 / 4096 ) =

18 * 4095 / 4096 =

73710 / 4096 =

17.99560546875
a = 9 , r = 1 / 2 , n = 12