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
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
4 answers