The first three terms of a sequence are `3,1,-1`. The next terms is

Options

A. `2`
B. `-3`
C. `-(5)/(27)`
D. `-(5)/(9)`

Answer

B

Explanation

The given sequence is not an AP or GP or HP. It is an AGP,`3,(3+d)r,(3+2d)r^(2),"…."`
`implies (3+d)r=-1,(3+2d)r^(2)=-1`
Eliminating r, we get `(3+d)^(2)=-(3+2d)`
`implies d^(2)+8d+12=0 implies d=-2,-6`
then `r=-1,(1)/(3)`
`:.` next term is `(3+3d)r^(3)=3,-(5)/(9)`