Question

Find the sum of the first 11 terms of the geometric sequence shown below.
-3/2, 3, -6, 12...

Answer 1

`a_1=-(3)/(2)`

`a_2=3`


`q=3:(-(3)/(2))=3*(-(2)/(3))=-2`


`S_(11)=-(3)/(2)*(1-(-2)^(11))/(1+2)`

`S_(11)=-(3)/(2)*(1-(-2048))/(3)`

`S_(11)=-(3*2049)/(2*3)`

`S_(11)=-(2049)/(2)`

`S_(11)=-1024(1)/(2)=-1024,5`

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