SOLUTION: Hello, I am stuck with this problem and cannot seem to find any help. I need to find s6 of a geometric sequence. Given are {{{b3 = 9}}} and {{{b6= -64/3}}} I know to find the

Algebra ->  Sequences-and-series -> SOLUTION: Hello, I am stuck with this problem and cannot seem to find any help. I need to find s6 of a geometric sequence. Given are {{{b3 = 9}}} and {{{b6= -64/3}}} I know to find the      Log On


   

Question 481797: Hello, I am stuck with this problem and cannot seem to find any help.
I need to find s6 of a geometric sequence. Given are b3+=+9 and b6=+-64%2F3
I know to find the sum I would need to use sn=a1%2A%281-r%5En%29%2F%281-r%29 but for that I would need the 1st term of the sequence. I simply do not know how I can find the common ratio to find the first sequence and an=a1%2Ar%5En-1 is not helping me there since I have 2 unknown.
Thank you a lot
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

geometric sequence

a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29

b%5B3%5D=a%5B1%5Dr%5E2=+9  a%5B1%5D = 9/r^2

b%5B6%5D=a%5B1%5Dr%5E5=+-64%2F3%29

         %289%2Fr%5E2%29r%5E5+=+%28-64%2F3%29

                   r^3 = -64/27 

                     r= -4/3   and a%5B1%5D=+9%2F%28-4%2F3%29%5E2+=+81%2F16

s%5Bn%5D=a1%2A%281-r%5En%29%2F%281-r%29 

  s%5B6%5D=+%2881%2F16%29%2A%281-%28-4%2F3%29%5E6%29%2F%287%2F3%29